An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses. H0: The product does not change the height of the plant. Ha: The product makes the plant grow taller. Is the following an example of a type I or type II error? The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.

Answers

Answer 1

Answer:

hi

Step-by-step explanation:

hji


Related Questions

Use the probability distribution table to answer the question.
What is P(1 < X < 5)?
Enter your answer, as a decimal, in the box.

Answers

Answer: 0.51

Add up the P(x) values that correspond to x = 2 through x = 4

0.07+0.22+0.22

So we have a 51% chance of getting an x value such that 1 < x < 5

By using the probability distribution table, the value of P(1<x<5) is 0.51

What is Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true

What is Probability distribution?

A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events

Given,

We have to find the value of P(1<x<5)

P(1<x<5) = P(2)+P(3)+P(4)

P(2)=0.07

P(3)=0.22

P(4)=0.22

P(1<x<5) = 0.07+0.22+0.22 =0.51

Hence, the value of P(1<x<4)= 0.51

Learn more about Probability and Probability distribution here

https://brainly.com/question/14210034

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Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?

Answers

Answer:

92 inches squared

Step-by-step explanation:

T/P = 8 * 3

L/R = 3 * 2

F/B = 8 * 2

Solving for surface area!

2(24) + 2(6) + 2(16) = 92

in the diagram, find the values of a and b.​

Answers

Answer:

           m∠a = 67° ,   m∠b = 42°

Step-by-step explanation:

∠a is alternate interior angle to ∠ECD

∠b is alternate interior angle to ∠BCD

so:

If AB || CD then:

m∠a = m∠ECD = 25° + 42° = 67°

m∠b = 42°

Solve x2 + 9x + 8 = 0 by completing the square. What are the solutions?
O (1.-8)
O (1.8)
O (-1-8)​

Answers

Answer: (-1,-8)

Explanation:

x^2 + 9x + 8 = 0
x^2 + 9x = -8

Add (9/2)^2 to both sides

x^2 + 9x + (9/2)^2 = -8 + (9/2)^2
(x + 9/2)^2 = -8 + 81/4
(x + 9/2)^2 = -32/4 + 81/4
(x + 9/2)^2 = 49/4

Square root both sides

Sqrt (x + 9/2)^2 = sqrt 49/4
x + 9/2 = plus or minus 7/2

Set x + 9/2 = 7/2:

x + 9/2 = 7/2
x = 7/2 - 9/2
x = -2/2 = -1

Set x + 9/2 = -7/2:
x + 9/2 = -7/2
x = -7/2 - 9/2
x = -16/2 = -8

A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles.​ Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.

Compute the linear speed on the surface of the planet at 30 degrees north latitude.

Answers

Answer:

The velocity is  [tex]v = 886.96 \ m/s[/tex]

Step-by-step explanation:

From the question we are told that

    The period of each revolution is  [tex]T = 1\ day = 24 \ hours[/tex]

    The angle  is [tex]\theta = 30^o[/tex]

     The radius is  [tex]r = 3387.5 \ miles[/tex]

Generally the linear speed is  mathematically represented as

        [tex]v = w * r[/tex]

Where  [tex]w[/tex] is the angular speed which is mathematically represented as

       [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

       [tex]w = \frac{2 *3.142 }{24}[/tex]

        [tex]w = 0.2618 \ rad/s[/tex]

Thus  

         [tex]v = 0.261833 * 3387.5[/tex]

        [tex]v = 886.96 \ m/s[/tex]

     

Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.

Answers

Answer:

Its 10x^2+12

Step-by-step explanation:

Answer:

-10X^2+12

Step-by-step explanation:

Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.

Answers

Correction:

P(AΔB) = P(A) + P(B) - 2P(AnB)

is what could be proven using the axioms of probability, and considering the case of symmetric difference given.

Answer:

P(AΔB) = P(A) + P(B) - 2P(AnB)

Has been shown.

Step-by-step explanation:

We are required to show that

P(AUB) = P(A) + P(B) - 2P(AnB)

directly using the axioms of probability.

Note the following:

AUB = (AΔB) U (AnB)

Because (AΔB) U (AnB) is disjoint, we have:

P(AUB) = P(AΔB) + P(AnB)..................(1)

But again,

P(AUB) = P(A) + P(B) - P(AnB)...............(2)

Comparing (1) with (2), we have

P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)

P(AΔB) = P(A) + P(B) - 2P(AnB)

Where AΔB is the symmetric difference of A and B.

Question 15 please and i will mark the brainliest!!! And thank you to whoever answers

Answers

Answer: C) 12

Explanation:

We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?

Answers

Answer:

The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 500[/tex]

     The standard deviation is  [tex]\sigma = 100[/tex]

The  percent of people who write this exam obtain scores between 350 and 650    

    [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]

Generally  

               [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

   [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]

   [tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]

   [tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]

From the z-table  [tex]P(Z < -1.5 ) = 0.066807[/tex]

   and [tex]P(Z < 1.5 ) = 0.93319[/tex]

=>    [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]

=>  [tex]P(350 < X 650 ) = 0.866[/tex]

Therefore the percentage is  [tex]P(350 < X 650 ) = 86.6\%[/tex]

Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.

Answers

Answer:

c. It does not appear to be within statistical control because there is an upward trend.

Step-by-step explanation:

Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.

The one-sample z test is: a. a hypothesis test b. used to test hypotheses c. concerning a single population with a known variance d. concerning at least one population e. concerning the variance in a population d. all of the above

Answers

Answer:

d. all of the above

Step-by-step explanation:

A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used

Write down the name of the shape for question D. Please help!

Answers

Step-by-step explanation:

thats shape is a delta

:)

Answer:

arrow head

Step-by-step explanation:

Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?

Answers

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490     {means that the population mean is different from 490}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_1_4[/tex]

where, [tex]\bar X[/tex] = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

Yelena needs to swim a total of 8 miles this
week. So far, she swam 5 miles. Use the
equation 5 + m=8 to find how many more
miles Yelena needs to swim.

Answers

Answer:

3 miles

Step-by-step explanation:

5 + m=8

Subtract 5 from each side

5-5 + m=8-5

m = 3

She needs to swim 3 more miles

Answer:

Yelena needs to swim 3 more miles

Step-by-step explanation:

You need to solve for the variable "m", which represents the miles. Based on the information, Yelena swam 5 miles and she needs to swim 8. Solve:

[tex]5+m=8[/tex]

To find the value of m, you need to isolate it on one side of the equation. To do this, you need to get the 8 and 5 on the same side of the equal operation. For this, you need to use reverse operations. This undoes the value from one side and does the same on the other, keeping the equation balanced. Since we have a "positive 5", we take the opposite, which would be a "negative 5". So subtract 5 from both sides of the equation:

[tex]5-5+m=8-5[/tex]

Simplify. The 5's cancel each other out, leaving 0. 8-5 is 3:

[tex]m=3[/tex]

The total miles left that Yelena needs to swim is 3 miles.

:Done

a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit

Answers

Answer:

 $900

Step-by-step explanation:

To begin with let us estimate the total cash value of the prices

$1000 x 1= 1000

$500 x 1=  500

$50 x 2= 100

Total = $1600

Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets

2.5*1000= $2,500

Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600

Then the expected profit is = $2,500-$1600= $900

Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30? 30n + 60 > 150 30n + 60 150

Answers

Answer:

150<60+30n

Step-by-step explanation:

150 is the maximum amount that she can spend on gas. (which is the total)

she already spend $60

each fill up (n) costs 30

Answer:

the answer is B)

Step-by-step explanation:

as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall​

Answers

Answer:

  0.4 meters

Step-by-step explanation:

The volume is ...

  V = LHB

  12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values

  0.064 m³ = B³ . . . . . simplify

  ∛0.064 m = B = 0.4 m

The breadth of the wall is 0.4 meters.

5/7 minus 2/9 please

Answers

Answer:

[tex]\large \boxed{31/63}[/tex]

Step-by-step explanation:

5/7 - 2/9

Make denominators equal by LCM.

(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)

45/63 - 14/63

Subtract fractions since denominators are equal.

(45 - 14)/63

31/63

Answer:

[tex]\frac{31}{63}[/tex]

Step-by-step explanation:

Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]

Therefore, the answer is [tex]\frac{31}{63}[/tex].

Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is

Answers

Answer:

The true true level of significance of this test is more than 0.01.

Step-by-step explanation:

No standard deviation and we are told that the investigator still used z rather than the more appropriate t - distribution.

This method of using the z-distribution when standard deviation is unknown will definitely result in a smaller critical value and this in turn simply means that the p-value will be smaller than what it should really be.

Thus, it means the critical value is getting closer to the mean value than the way it should be.

Therefore, means that for a given significance of 0.01 and using the z-distribution under this no standard deviation situation, the true true level of significance of this test is more than 0.01.

name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)

Answers

Answer:

Step-by-step explanation:

Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.

- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.

∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]

- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.

∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]

- Angles having the same relative positions at the point of intersection are the corresponding angles.

∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]

- Co interior angles are the angles between the parallel lines located on the same side of the transversal.

∠4 and ∠5, ∠3 and ∠6 [Co interior angles]

- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.

∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]

Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)

Answers

Question Completion:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Answer:

Century Roofing

Project's NPV is: ($6,578)

Step-by-step explanation:

a) Data and Calculations:

WACC = 10.0%

Opportunity cost = $100,000

Net equipment cost (depreciable basis) = $65,000

Straight-line deprec. rate for equipment = 33.333%  

Sales revenues, each year = $123,000

Operating costs (excl. deprec.), each year = $25,000

Tax rate = 35%

Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)

Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700

PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)

NPV = Cash inflow minus Cash outflow

= $158,422 - $165,000

= ($6,578)

Negative NPV

b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value.  It becomes a present cash outflow.  Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.

3
BO
Evaluate the function f(x) = x2 + 4x + 1 at the given values of the independent variable and simplify.
a. f(6)
b. f(x +9)
c. f(-x)

Answers

Answer:

a) f(6)=(6)^2+4(6)+1=65

b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117

f (-x)=(-x)^2-4x+1

A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design

Answers

Answer:

Option A (repeated measures design) is the correct option.

Step-by-step explanation:

Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.

The other three options are not related to the given instance. So that alternative A would be the correct choice.

The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.

Answers

Answer:

To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.

Hope this helped!

36x7 please EXPLAIN the process of the multiplication plse

Answers

36×7

=252

Explaination :

First Multiply 6 and 7 we get 42 !

Write 2 and 4 will be added to the product of 3×7

We get 21 and add 4 here

So we get 252

Answer:

[tex]36 \times 7 = 252[/tex]

Step-by-step explanation:

Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.

Hope it helps u mate

What would be the mass of a cube of tungsten (density of 19.3 g/cm), with sides of
3cm?

Answers

Answer:

M= 521.1 g

Step-by-step explanation:

1st.  Find the volume of the cube:   V=3³=27 cm³

As the weight of V= 1 cm³ cube  is 19.3 g the weight of the cube=27 cm³ is

M=27*19.3= 521.1 g

3x18 = 3 (10+8) is an example of the _________ property of multiplication.

Answers

Answer:

3x18 = 3 (10+8) is an example of the commutative property of multiplication

Step-by-step explanation:

Answer: commutative property of multiplication

Step-by-step explanation:

A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students

Answers

I think the answer is 441 ft I’m sorry if it’s wrong

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years

Answers

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.Required:a. What is the (approximate) probability that X is at most 30?b. What is the (approximate) probability that X is less than 30?c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?

Answers

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]

                                                                  = 4.42

So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5)    {using continuity correction}

        P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5)   {using continuity correction}

       P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852

       P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.

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