Answer:
d. 0.0047
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
We have that [tex]\mu = 7.7, \sigma = 0.2[/tex]
Sample of 3:
[tex]n = 3, s = \frac{0.2}{\sqrt{3}} = 0.1155[/tex]
Which of the following represents the probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams?
This is 1 subtracted by the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 7.7}{0.1155}[/tex]
[tex]Z = 2.6[/tex]
[tex]Z = 2.6[/tex] has a pvalue of 0.9953
1 - 0.9953 = 0.0047
The probability is given by option d.
You can calculate the z score for the specified sample and then use the z tables to find the p value(probability) needed.
The probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams is given by
Option d : 0.0047
How to find the z score for a sample taken from a normal distribution holding random variate?Suppose that the sample is of size 'n', then we have the z score(we are converting random variable X to standard random variable Z) as:
[tex]Z = \dfrac{X - \overline{x}}{s} = \dfrac{X - \mu}{\sigma/\sqrt{n}}[/tex]
where [tex]\overline{x}[/tex] is mean of the sample
s is the standard deviation of the sample,
and we used the central limit theorem which says that a sample from a normally distributed population with [tex]mean = \mu[/tex] and standard deviation = [tex]\sigma[/tex] can have its mean approximated by population mean and its standard deviation approximated by [tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
Using the data given to find the intended probabilityLet the weight of the the olives for the given crop of olives of a particular company for taken random sample is given by X (a random variable)
Then, we have:
[tex]X \sim N(7.7, 0.2)[/tex]
where
[tex]\mu = 7.7, \sigma = 0.2[/tex]
Thus, we have:
[tex]\overline{x} = \mu, s = \sigma/\sqrt{n} = 0.2/\sqrt{3}[/tex]
Using the given facts, we get the needed probability as:
[tex]P( X> 8)[/tex] sample size n = 3)
Then, using the z score, we get):
[tex]P(X > 8) = 1 - P(X \leq 8) = 1 - P(Z \leq \dfrac{8 - 7.7}{0.2/\sqrt{3}})\\\\P(X > 8)=1- P(Z \leq \dfrac{0.3\sqrt{3}}{0.2}) = 1- P(Z \leq 1.5 \times \sqrt{3} )\\\\P(X > 8) = 1 - P(Z \leq 2.59) = 1- 0.9952 \approx 0.0047[/tex]
Thus,
The probability that the mean weight of a random sample of 3 olives from this population is greater than 8 grams is given by
Option d : 0.0047
Learn more about standard normal distribution here:
https://brainly.com/question/14989264
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable. 2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice. 3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote.
4. If Kevin wrote 21 posts, how many did Cheryl write?
Answer:
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable. (2 points)
The expression will be P for "of posts Kevin writes."
2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice. (2 points)
The operation I will use is subtraction so P-7.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote. (3 points)
Subtraction would be the operation and my expression would be ( P-7 ) which would also be ( 21 - 7 )
4. If Kevin wrote 21 posts, how many did Cheryl write? (3 points)
Cheryl wrote 14 posts, because 21 - 7 = 14
Hope this helps <3
1. We have chosen a variable 'x' to represent the number of posts by Kevin.
2. Subtraction applies to this situation.
3. The number of posts written by Cheryl is (x - 7).
4. If Kevin wrote 21 posts, Cheryl wrote 14 posts.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, Kevin writes 'x' number of posts,
Therefore, Cheryl writes (x - 7) posts.
We could have chosen any letters for the number of posts Kevin writes,
And as Cheryl writes fewer posts than Keving we subtracted the number.
If Kevin writes 21 posts, 'x' is 21, And hence Cheryl has written,
(21 -7).
= 14 posts.
learn more about equations here :
https://brainly.com/question/10413253
#SPJ1
solve the following problem. round to one decimal place if necessary. if your answer is correct you will see an image appear on your screen
Answer:
theres no picture
Step-by-step explanation:
Use this table to answer questions below. Choose the correct answer.
According to the line graph, between 1950 and 1970 approximately which year had the lowest percentage of business failures?
Answer:
The answer is 1954
Step-by-step explanation:
Answer:
1954
Step-by-step explanation:
It is the lowest percentage of business failures. Refer to the scale on the left.
Armando has 3 blue shirts, 3 green shirts,
and 2 red shirts. He has 3 pairs of jeans
and 4 pairs of cargo pants. He is equally
likely to wear any of the shirts with any
pair of pants. What is the probability that
Armando will wear a green shirt with cargo pants?
Answer:
0.2143 = 21.43% probability that Armando will wear a green shirt with cargo pants.
Step-by-step explanation:
Probability:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of independent events:
The probability of two independent events is the multiplication of their separate probabilities.
Green shirt:
3 green shirts, out of 3 + 3 + 2 = 8 shirts.
So 3/8 probability of green shirts.
Cargo pants:
4 cargo pants, our of 4 + 3 = 7.
So 4/7 probability of cargo shirts.
Green shirt and cargo pants:
[tex]p = \frac{3}{8} \times {4}{7} = \frac{12}{56} = \frac{3}{14} = 0.2143[/tex]
0.2143 = 21.43% probability that Armando will wear a green shirt with cargo pants.
177 is what percent of 300? Round your answer to the nearest tenths.
Answer: 59%
Step-by-step explanation:
Hope this helps have a great day. :)
Answer:
59%
Step-by-step explanation:
I would solve this through proportions
177 x
300 100
Cross multiply
177 x 100 = 17700
And then divide
17700/300 = 59
The answer is 59%
Please solve this for 15 points explain please
Answer:
1.25 cups
Step-by-step explanation:
Since you have 5 5/8 cups = 4 1/2 water bottles
you can make it
5.625 cups = 4.5 water bottles
Then, all you have to do is divide both sides of this equation by 4.5, so
5.625 / 4.5 = 1 water bottle
1.25 cups = 1 water bottle
PLEASE HELP
HELP
ILL MARK BRAINLIEST
HELP
HELP
PLEASE HELPP
Answer:
D
Step-by-step explanation:
The others don't work as it would if it was the older men
maria and emme each had 4 pints of paint on the first day of painting maria used 3/5 of her 4 pints amd emma used 3/4 of her 4 pints of paint altogether how much of maira and emma paint remained altogether how much of maria and emme paint remained after the first day of painting
HEELLPP ME PLZZZ
Answer:
[tex]\frac{13}{5}[/tex] pints of paints are left together
Step-by-step explanation:
Given
Number of pints of paint with Maria [tex]= 4[/tex]
Number of pints of paint with Emme [tex]= 4[/tex]
On the first day , Maria used [tex]\frac{3}{5}[/tex] of her [tex]4[/tex] pints of paints
Hence, Paint left after first day with Maria
[tex]= 4 - (\frac{3}{5} * 4)\\= \frac{20 - 12}{5} \\= \frac{8}{5}[/tex]
On the first day , Emme used [tex]\frac{3}{4}[/tex] of her [tex]4[/tex] pints of paints
Hence, Paint left after first day with Emme
[tex]= 4 - (\frac{3}{4} * 4)\\\\= 4-3\\= 1[/tex]
Total pint of paint left with both Maria and emme altogether
[tex]= 1 + \frac{8}{5}\\= \frac{5+8}{5} \\= \frac{13}{5}[/tex]
Which answer is a solution for x?
X/7= 8
A 8
B 15
C 48
D 56
HELP MEH PLS PLS ASAP PLEASE
Please help. find the missing side of each triangle
Answer:
x = √146 = 12.1 (nearest tenth)
Step-by-step explanation:
Apply pythagorean theorem, c² = a² + b², where,
c = x
a = √82 km
b = 8 km
Plug in the values
x² = (√82)² + 8²
x² = 82 + 64
x² = 146
x = √146 = 12.1 (nearest tenth)
What lines are perpendicular to 3x+6y=5
Answer:
u means that to make the equations
Answer:
the line on the point 1.2 and 4.5
Step-by-step explanation:
Which equation represents a line with a slope of -8 and
a y-intercept of 4?
y = -8x4
y = - 4x +8
y = -8x4
y = 8x+4
The equation y = -8x + 4 represents the given problem.
What is slope and y-intercept?'The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis.'
According to the given problem,
We know,
Equation of a line can be represented as,
y = mx + c, where, m = slope
c = y-intercept
Slope of the line = -8
Y-intercept of the line = 4
Therefore,
The equation of the line:
⇒ y = -8 + 4
Hence, we can conclude, the equation y = -8x + 4 represents the given line.
Learn more about slope and y-intercept here: https://brainly.com/question/20639041
#SPJ2
Jackson has up to 7 1/2 hour to spend at an amusement park he will spend 1 1/2 of those hours at the water park He will spend x hours at each of the 3 other sections in the amusement park.
Select the inequality that can be solved to determine the number of hours Jackson can spend in each one of the other sections.
A. 1 1/2 + 3 ≤ 7 1/2
B. 3X + 1 1/2 ≥ 7 1/2
C, 1 1/2x + 3 ≥ 7 1/2
D. 3x + 1 1/2 ≤ 7 1/2
Plz right answer
Answer:
D
Step-by-step explanation:
Since Jackson has 7 1/2 hours to spend at the amusement park, he has already spent 1 1/2 of those hours at the water park (We will need this shortly). Since he has 6 hours remaining and 3 parks to go, he can't spend more than 7 1/2 hours at the park. This means that the answer will have to be less than or equal to. Finally, it would be D because he can spend any amount of time at the other 3 parks (x) plus the 1 12 hours he already spent.
quadrilateral ABCD is a kite with an area of 14cm squared. the length of ED is 5 cm. what is the length of BE?
Answer:
85
Step-by-step explanation:
The length of BE is 5.6 cm.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
The area of a kite can be calculated as;
A = d1 x d2 / 2
WE are given the parameters as;
d1 = ED = 5 units
A quadrilateral ABCD is a kite with an area of 14cm squared.
Therefore,
14 = 5 x BE / 2
14 x 2 = 5 BE
28 = 5 BE
BE = 5.6 cm.
Learn more about quadrilaterals here:
https://brainly.com/question/1365755
HELP IM TIMES FOR 20 MINUTES! IVE BEEN ON THIS FOR THE LONGEST!
Answer:
Point d
Step-by-step explanation:
because the x is -2 and the y is 3 so you look for the x and then the y
Driving would be more pleasant if we didn't have to put up with the bad habits of other drivers. A newspaper reported the results of a Valvoline Oil Company survey of 500 drivers in which the drivers marked their complaints about other drivers. The top complaints turned out to be tailgating, marked by 22% of the respondents; not using turn signals, marked by 19%; being cut off, marked by 14%; other drivers driving too slowly, marked by 9%; and other drivers being inconsiderate marked by 5%.
Required:
Make a Pareto chart showing percentage of drivers listing each stated complaint.
Answer and Explanation:
The Pareto chart is used in descriptive statistics and shows graphically the most frequent occurencies(complaints in this case) using bars and lines.
Please find attached
Find the value of the power.
7^4 =
Answer:
Answer:
2401
Step-by-step explanation:
7*7*7*7=2401
Answer:
28
Step-by-step explanation:
(-Z - 8) - (62-5)
Help me please thank
Answer: -z-65
Step-by-step explanation:
Linda purchased 1½ pounds of potatoes on Friday and 2⅓ pounds of potatoes on Saturday. What was the total weight, in pounds, of potatoes purchased by Linda in the two-day period?
I need help finding the area of this shape can you please help
Answer: 139.27
Step-by-step explanation:
So let find the area of the black swuare the length is 10 and the widith is 10, using bxh the area is 100. Now let find the aea of the semi-circle. The area of a fill circle is pi radius squared so a semi circle area will be 1/2( pi radius squared). The radius is 5 so we can calculate 1/2 of 25 pi equal = 39.27. Now let add the areas: 100+39.27=139.27.
simplify: (2x^2y^3)3 x (4xy)2
Answer: 48yx^1+2y^3
Step-by-step explanation:
Will give brainliest
Answer:
.c
Step-by-step explanation:
Starting at 1:00 p.M., The temperature changes -4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours (x) it will take to reach -1 °F. please say the equation.
Answer:
0.25 hours
Step-by-step explanation:
The equation for a linear function is given by:
y = mx + b,
where y and x are variables, m is the rate of change of y with respect to x and b is the initial value of y (value of y when x = 0).
Let x represent the number of hours after 1:00 P.M and let y represent the temperature in degree Fahrenheit.
Let us assume that initial the temperature is 0°F. The temperature changes -4 degrees Fahrenheit per hour. From the equation of a linear function y = mx + b:
m = -4 degrees Fahrenheit per hour, b = 0. Hence:
y = -4x
The time taken to reach -1°F is gotten by substituting y = -1 and finding x:
y = -4x
substituting:
-1 = -4x
x = -1 / -4
x = 0.25 hours
0.25 hours = 0.25 hours * 60 minute / 1 hour = 15 minute
Therefore at 1:15 P.M, the temperature is -1°F
if you help i will say thank you
Answer:
C
Step-by-step explanation:
(5,-4)
Answer:
C
Step-by-step explanation:
(5,-4) by using elimination method
1. In each of the following expressions, c represents the original cost of an item.
10.900
TL 0.10c
C -0.10c
a. Circle the expression(s) that represents 10% of the original cost. If more than one is
correct explain why the expressions you chose are equivalent.
represents ® D
b. Put a box around the expression(s) that represent the final item after a 10% decrease.
If more than one is correct explain why the expressions you chose are equivalent.
2. An item that was selling for $72.00 is reduced to $60.00. Find the percent decrease in
price. Round your answer to the nearest tenth.
3. A baseball team had 80 players shows up for tryouts last year and this year 96 players
show up for tryouts. Find the percent increase in players from last year to this year.
4. The price of a bag of bagels rose from $2.80 in January to $3.50 in April. What was the
percent increase of the price of a bag of bagels?
A 20%
B. 25%
C. 70%
D. 80%
5. Joe's weekly pay increased from $80 to $100. What is the percent increase in pay?
A 40%
B. 25%
C. 20%
D. 80%
Plzzzzz help
What are the solutions to x2 – 10x = 39?
Answer: x=−3 or x=13
Step-by-step explanation:
Step 1: Subtract 39 from both sides.
x2−10x−39=39−39
x2−10x−39=0
Step 2: Factor left side of equation.
(x+3)(x−13)=0
Step 3: Set factors equal to 0.
x+3=0 or x−13=0
x=−3 or x=13
the triangles below are similar.
Answer: 54
Step-by-step explanation:
Since the triangles are similar, the sides form s equalivent proportion. The hypotunse of the bigger triangle and the smaller triangles correspond with each other and the base of the smaller and larger triangle correspond so we use this proportion: hypo. of big triangle/ base of larger triangle= hypo of smaller triangle/ base of smaller triangle.
Let substitue: 52.5/x= 5/4: ( I Reduce 15/12 into 5/4).Cross multiply: 210=5x: Divide by 5 both sides. x=42. Then add the 42 and and the 12 to find the whole distance which is 54.
If there is 60 runners and they each get 8 oz of water how many pounds of water do they get total
PLEASE HELP !
I AM RUNNING OUT OF TIME
Answer:
149
Step-by-step explanation:
If you order the numbers from smallest to biggest and then find the middle number it is 149
Answer:
Median is 149
Step-by-step explanation:
just sum extra info lol<3
min is 144
mean is 150
max is 160
so in order: 144,145,147,148,149,150,152,155,160
hope i could help:)
X-8-3X-10
Use distributive property
Answer:
5x-10
Step-by-step explanation:
8x-3x-10
first you subtract 3from 8 and get 5 just add the x so your left with 10
Answer:
-2(x+9)
Step-by-step explanation:
x-8-3x-10
-4x-18
-2(x+9)
Hope it helps you
