A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.

Answers

Answer 1

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9


Related Questions

In complete sentences explain how you would factor the numeric expression 34 + 12 + 20.

Answers

Answer:

We are asked to determine the correct factorization of the given trinomial which is 5x² - 5x -100. The solution to this problem is shown below:

5x² - 5x - 100 let the problem equal to zero such as:

5x² - 5x - 100 = 0 , factor out 5 from the given trinomial

5(x²-x-20) = 0

5 (x-5)(x+4) = 0

The correct factor is 5(x-5)(x+4).

Step-by-step explanation:

I need help please help me! I don’t understand this

Answers

Answer:

170 m³

Step-by-step explanation:

To solve this type of problem, assume you have two solids joined together to make the shape you have up there. This will enable you find the volume of each, then sum both volume together to get your answer.

Let's solve for the volume as follows.

If we divide the solid into 2, what we have is 2 cuboid: the first having dimensions of:

length (l) = 6m,

width (w) = 2m,

height (h) = 8m

Volume of the first cuboid = [tex] l*w*h = 6*2*8 = 86 m^3 [/tex]

The second cuboid:

length (l) = 7m,

width (w) = 6m,

height (h) = 2m

Volume of the first cuboid = [tex] l*w*h = 7*6*2 = 84 m^3 [/tex]

Volume of the figure = 86 + 84 = 170 m³

A survey of 1,565 households estimated that 72% of the households in a given state owned a television. What is the population? all the households in given state 1565 households surveyed 1127 households that owned televisions

Answers

Answer:

all the houses in given state

Step-by-step explanation:

edge 2021

Using sampling concepts, it is found that the population is given by:

All the households in given state.

What is a sampling?

In a sampling, data is taken from a sample to be estimated for the entire population.

For example, if you want to find the proportion of New York State residents that are Buffalo Bills fans, surveying a sample of 1000 residents, the population is all New York State residents.

Hence, in this problem, the population is given by all the households in given state.

More can be learned about sampling concepts at https://brainly.com/question/25122507

Which statement about the angle measures is true?
m_BAC + m2 ACB 85
m.BAC MACB 95
95°
m..BACA BC 85
m. BACIMBC 95
B

Answers

Answer:

Option (4)

Step-by-step explanation:

By the property of exterior angle of a triangle,

"Exterior angle of a triangle is equal to the sum of two opposite interior angles."

In the triangle ABC,

∠ACD is an exterior angle and ∠BAC and ∠ABC are the opposite interior angles.

m∠ACD = m∠BAC + m∠ABC

95° = m∠BAC + m∠ABC

Therefore, Option (4) will be the correct option.

Reduce the following fraction to lowest terms: 8/14

Answers

Answer:

4/7

Step-by-step explanation:

divide both by two for its simplest form

Answer:4/7

Step-by-step explanation

Divide both the numerator and denominator by 2

The result for the numerator is 8/2=4

that of the denominator is 14/2=7

Therefore the resultant answer is 4/7

If you conducting a test for statistical study and you got outcome with the likelihood of 0.005. Please evaluate outcome.

Answers

Here is the complete question:

a. Statistically significant at 0.01

b. Not statistically significant

Answer:

The test is significant

Step-by-step explanation:

When a p value is smaller than or less than alpha we say it is statistically significant.

We are testing the p value or likelihood of 0005 against a significant level of 0.01

P value = 0.005 < 0.01

0.005 is less than 0.01 which shows the test to be significant.

The decision rule would be to reject the null hypothesis and say the result is statistically significant.

When the scale factor is one what is the ratio of the side length of the side opposite angle a and the length of the hypotenuse

Answers

Answer:

me ajuda por favor matemática

Hunda Corporation’s expected year end dividend amounting to RM1.60, and its required return is 11 percent. The dividend yield is 6 percent and its growth rate is expected to be constant in the future. What is Hunda Corporation’s expected stock price in 7 years?

Answers

Answer:

Hunda expected stock price in 7 years = RM48.12

Step-by-step explanation:

expected year end dividend = RM1.60

required return = 11%

dividend yield = 6%

growth rate = constant

Determine Hunda corporation's expected stock price in 7 years

stock price in 7 years

= expected year end dividend / (required return rate - dividend yield rate )

= 1.6 * (1.06)^7  / ( 0.11 - 0.06 )

= 2.4058 / 0.05 =  48.12%

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

Answers

Answer:

The critical value is 6.26.

Step-by-step explanation:

It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.

The critical value of F to test the significance of the model is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

Here,

k = number of independent variables

n = number of observations.

Then the critical value is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

                      [tex]=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26[/tex]

*Use a F-table.

Thus, the critical value is 6.26.

average of 2721 2557 2999 2278 4339

Answers

Answer:

Step-by-step explanation:

So we know that the average of numbers is all of the numbers added up and divided by the total amount of numbers.

      2721

   + 2557

-------------------

       5278

.... AND SO ON.........

=14,894 is all of the number added together!!!

Then we count up the numbers= 5

       14,894/5

=2978.8

I hope this helps!!!

mortician math word problem

Answers

Answer:

wat do u want me to do

Step-by-step explanation:

602/100 into a decimal describe plz

Answers

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Brainly help me Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass? Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.

Answers

Answer:

1/3

Step-by-step explanation:

1[tex]\\1\frac{2}{5} =1.4\\\\[/tex]

[tex]1\frac{3}{5} =1.6[/tex]

[tex]1.6+1.4=3[/tex]

3 Liters of Fruit Punch.

3/9=1/3 Fruit Punch among the 9 glasses.

In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?

Answers

Answer:

Yes it is reasonable to conclude the mean rate charged is greater than 14%

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 0.14[/tex]

    The sample size is  [tex]n = 10[/tex]

    The  sample mean is  [tex]\= x = 0.1564[/tex]

     The  standard deviation is  [tex]\sigma = 0.01561[/tex]

     The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is    [tex]H_o: \mu = 0.14[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 0.14[/tex]

 Generally the test statistic is mathematically represented as

              [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]

              [tex]t = 3.322[/tex]

Now the p-value obtained from the z-table is

        [tex]p-value = P(t > 3.322) = 0.00044687[/tex]

Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that  the mean rate charged is greater than 14%

 

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  [tex]H_o : \mu = 122[/tex]

the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

The test statistics is  [tex]t = - 1.761[/tex]

The p-value is  [tex]p = P(Z < t ) = 0.039119[/tex]

so

    [tex]p \ge 0.01[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 122[/tex]

     The sample size is  n=  38

    The sample mean is  [tex]\= x = 116 \ feet[/tex]

     The standard deviation is [tex]\sigma = 21[/tex]

     

Generally the null hypothesis is  [tex]H_o : \mu = 122[/tex]

                the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

Generally the test statistics is mathematically evaluated as

         [tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]

substituting values

         [tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]

         [tex]t = - 1.761[/tex]

The p-value is mathematically represented as

      [tex]p = P(Z < t )[/tex]

From the z- table  

     [tex]p = P(Z < t ) = 0.039119[/tex]

So  

     [tex]p \ge 0.01[/tex]

 

         

     

           

Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 Determine the quartiles.

Answers

Answer:

Lower quartile= 4.75

Middle quartile= 9.5

Upper quartile= 14.25

Step-by-step explanation:

The given date set is 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

On counting them we notice that it's number of element is 18

So N = 18

Arranging them in ascending order gives

12,18,18,20,23,24,24,25,25,29,31,43,43,43,53,53,65,78

Lower quartile= (N+1)*1/4

Lower quartile= (18+1)/4

Lower quartile= 19/4

Lower quartile= 4.75

Middle quartile= (N+1)*2/4

Middle quartile= (18+1)*2/4

Middle quartile= (19)*2/4

Middle quartile= 9.5

Upper quartile= (N+1)*3/4

Upper quartile= (18+1)*3/4

Upper quartile= (19)*3/4

Upper quartile= 14.25

Inter quartile range = upper quartile- minutes lower quartile

= 14.25-4.75

= 9.5

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out - squares from each corner. The length of the original piece of cardboard is more than the width. If the volume of the box is , determine the dimensions of the original piece of cardboard.

Answers

Question is not complete, so i have attached it.

Answer:

Length = 30 inches

Width = 22 inches

Step-by-step explanation:

Let the width of rectangular sheet be x inches.

Let the length of the sheet be (x + 8) inches.

Now, after she cuts 4 inches squares from each corner, she will get a box of length: x + 8 - 4 - 4 = x inches , width: (x - 8) inches and height 4 inches.

Now, volume of a cube is;

V = lwh

Thus;

V = x(x - 8)(4)

We are told that the volume of the box is 2640 in³

Thus;

x(x - 8)(4) = 2640

Divide both sides by 4 to get;

x(x - 8) = 660

x² - 8x - 660 = 0

Using quadratic formula, we have;

x = 30 or - 22.

We will use x = 30 as the other one is negative.

Since we earlier deduced that she will get a box of will get a box of length: x inches , width: (x - 8) inches

Thus,

Length = 30 inches

Width = 30 - 8 = 22 inches

In the given diagram if AB || CD, ∠ABO = 118° ∠BOD = 152° then find the value of ∠ODC. please help !!!!!!

Answers

Answer: ODC = 90 degree

Explanation:

It looks like a right angle to me
So it should be 90 degree

Which best describes the relationship between the lines with equations -36x + 8y = 16 and
-9x + 2y = 4?

Answers

Hi there! :)

Answer:

The lines are the same.

Step-by-step explanation:

Begin by converting each equation into its simplest form in slope-intercept form:

-36x + 8y = 16

Move the "x" variable to the right side of the equation:

8y = 36x + 16

Divide all terms by 8:

y = 36/8x + 16/8

y = 9/2x + 2

-------------------------------

-9x + 2y = 4

Move "x" variable:

2y = 9x + 4

Divide both sides by 2:

y = 9/2x + 2

Both of the equations are equivalent, meaning both of the lines are the same.

How do I solve these equations:
sin(2θ) + sin θ = 0
sin(2θ) = sqrt 3 cos θ

for intervals 0=< θ < 2pi

Answers

Answer:

Step-by-step explanation:

Given that

sin(2θ)+sinθ=0

We know that

sin(2θ)=2 sinθ x cosθ

Therefore

2 sinθ x cosθ + sinθ=0

sinθ(2 cosθ+1)=0

sinθ= 0

θ=0

2 cosθ+1=0

cosθ= - 1/2

θ=120°

_______________________________________________________

[tex]sin 2\theta=\sqrt{3cos\theta}[/tex]

By squaring both sides

[tex]sin^2 2\theta={3cos\theta}[/tex]

4 sin²θ x cos²θ=3 cosθ

4 sin²θ x cos²θ - 3 cosθ=0

cos θ = 0

θ= 90°

4 sin²θ=3

θ=60°

Solve for X: 1+1*12/80-2+3=56x

Answers

Answer:

NOT SURE

Step-by-step explanation:

The range of values for x?

Answers

Answer:

x = 32

but

I would say anything from 30 to 33

but truly i have no clue about the range

Step-by-step explanation:

3x-9=87 (because 180 -93 =87)

3x = 96

x = 32

Answer:

it is 32

Step-by-step explanation:

Diane has a rectangular poster that is 20 centimeters long and 15 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.

Answers

Answer:

0.03 square meters

Step-by-step explanation:

1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively

2. calculate the area by multiply 2 numbers together

0.2 × 0.15 = 0.03 square meter

Robert, a ninth-grader, has just been told, "The reason you’re having so much trouble with division is that you have never mastered compound multiplication. The Math Basic Skills Tests have indicated this quite clearly. We are going to provide you with instruction in multiplication immediately." Robert’s teacher made what kind of decision relative to his skill level?

Answers

Answer:

Diagnostic

Step-by-step explanation:

The teacher made a diagnostic decision relative to Roberts skill level. Before she made this decision, she first started with the process of evaluation to know his strength and also establish his weakness. With the knowledge she has gotten she now plans to him with meaningful learning and an efficient curriculum that would help him in mastering multiplication first before division.

Solve 45 - [4 - 2y - 4(y + 7)] = -4(1 + 3y) - [4 - 3(y + 2) - 2(2y -5)] (make sure to type the number only - rounded to the tenth)

Answers

Answer:

Rounded: -5.5

Step-by-step explanation:

Work above :)

What is the value of 1 in 1,255 is what times the value of the 1 in 82,175

Answers

Answer:

100,000

You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.

Answer:

Step-by-step explanation:

2**2-5 what is answer of this equation

Answers

Answer:

[tex]\huge\boxed{-1}[/tex]

Step-by-step explanation:

=> 2 * 2 -5

Multiplying first according to DMAS rule

=> 4 - 5

=> -1

P.s. This is not an equation. This is an expression!

Answer:

[tex]\Huge \boxed{-1}[/tex]

Step-by-step explanation:

[tex]\Rightarrow 2 \times 2 -5[/tex]

Division and multiplication to be performed first.

[tex]\Rightarrow 4-5[/tex]

Addition and subtraction next.

[tex]\Rightarrow -1[/tex]

HELP ASAP HELP ASAP HELP ASAP HELP ASAP HELP ASAP HELP ASAP HELP ASAP HELP ASAP HELP ASAP

Answers

Answer:

Segment LM Corresponds to RQ    

Segment R corresponds to angle M

Answer:

Step-by-step explanation:

six hundred men,six hundred men with big mouths to feed

Evaluate m^2 − 2m + 5 for m = − 2

Answers

Answer:

[tex]\huge\boxed{13}[/tex]

Step-by-step explanation:

m²-2m + 5

Given that m = -2

[tex]\sf (-2)^2-2(-2)+5\\4 +4 + 5\\13[/tex]

Answer:

13

Step-by-step explanation:

m^2 − 2m + 5

Let m = -2

(-2)^2 -2(-2) +5

4 +4 +5

13

(4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000 (c) x 3 100 − 1000x 2 (d) x log x (2) (2 points) U

Answers

Answer:

(a) O(x²)

(b) O(x²)

(c) O(x²)

(d) Not O(x²)

Step-by-step explanation:

If a function is O(x²), then the highest power of x in the function ia greater or equal to 2.

(a) 100x + 1000

This is O(x), not O(x²)

(b) 100x² + 1000

This is O(x²)

(c) x³.100 − 1000x²

This is O(x²)

(d) x log x²

This is not O(x²)

Other Questions
The idea that chromosomes orient themeselves randomly during metaphase I is ________________________. This leads to ___________________ combinations of genes. Which number line represents the solution set for the inequality negative StartFraction one-half EndFraction x is greater than or equal to 4.x 4?A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the right. Which of these is true about electrons? posses a positive electrical charge of one (+1) have a negative electrical charge of one (-1) indicates the number of protons in each atom equals the sum of protons plus neutrons in each atom Modern farming methods require more inputs which are manufactured in industry. Do you agree? he said what is the matter convert into indirect speech Which is not a characteristic of a state? PLSSS HELP I would appreciate it Find the measure of a A. 44 B. 88 C. 46 D. 90 Communication is a dynamic proces s through we convey thought or idea.it comes from the woed 'communis' Considera Usted que las condiciones de vulnerabilidad ante un Tsunami son las mismas para todas las poblaciones? Justifique su respuesta con tres argumentaciones. Find the distance between the points P and Q shown. Question 6 options: A. 73 B. 13 C. 5 D. 65 Find the weight of a pine tree that has a circumference of 14 inches and a height of 120 feet. Use the equation: W = b0 + b1(D2H) why did columbus seize the town referred to in the document above? Corporation has found that % of its sales in any given month are credit sales, while the remainder are cash sales. Of the credit sales, Corporation has experienced the following collection pattern: 20% received in the month of the sale 40% received in the month after the sale 24% received two months after the sale 16% of the credit sales are never received November sales for last year were , while December sales were . Projected sales for the next three months are as follows: January sales. . . . . . . . . . . . . . . . $150,000 February sales. . . . . . . . . . . . . . . $130,000 March sales. . . . . . . . . . . . . . . . . $175,000 Requirement Prepare a cash collections budget for the first quarter, with a column for each month and for the quarter. (Round your answers to the nearest whole dollar.) Sweeney Corporation Cash Collections Budget For the Months of January through March January Cash sales Collections on credit sales: 20% Month of sale 40% Month after 24% Two months after Total cash collections Enter any number in the edit fields and then click Check An When the nuclide carbon-14 undergoes beta decay: The name of the product nuclide is . The symbol for the product nuclide is What is the issue with the work? It is wrong. Please answer this for points! Given the data: Ag2O(s), = 31.1 kJ mol-1, S = +121.3 J mol-1 K-1 Ag(s), = 0.00 kJ mol-1, S = +42.55 J mol-1 K-1 O2(g), = 0.00 kJ mol-1, S = +205.0 J mol-1 K-1 Calculate the temperature at which = 0 for the reaction, Ag2O(s) 2 Ag(s) + O2(g). Assume that, since the physical states do not change, and are independent of temperature between 50.0 C and 950.0 C. Name four breeds of cattle An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges? A sample of 36 observations is selected from one population with a population standard deviation of 4.2. The sample mean is 101.5. A sample of 50 observations is selected from a second population with a population standard deviation of 5.0. The sample mean is 100.1. Conduct the following test of hypothesis using the 0.10 significance level.H0 : 1 = 2H1 : 1 2a.This is a_________tailed test.b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)The decision rule is to reject H0 if z is ___________the interval.c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0?e. What is the p-value? (Round your answer to 4 decimal places.)