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Answer:

0.2605, 0.2188, 1.33, 4, 1.0540, 1.4142

Step-by-step explanation:

A fair die is rolled 8 times.  

a. What is the probability that the die comes up 6 exactly twice?  

b. What is the probability that the die comes up an odd number exactly five times?  

c. Find the mean number of times a 6 comes up.  

d. Find the mean number of times an odd number comes up.  

e. Find the standard deviation of the number of times a 6 comes up.  

f. Find the standard deviation of the number of times an odd number comes up.

a. A die is rolled 8 times. If A represent the number of times a 6 comes up. For a fair die the probability that the die comes up 6 is 1/6 - Thus A ~ Bin(8, 1/6)

The probability mass function  of the random variable A is  

hence, p(6 twice) implies P(A=2)

that is P(2) substitute A = 2

p(2) = 0.2605  

b. If B represent the number of times an odd number comes up. For the fair die the probability that an odd number comes up is 0.5.

Thus B ~ Bin(8, 1/2 )

The probability mass function of the random variable B is given by

hence p(odd comes up 5 times) is

p(5) = 0.2188

c. let the mean no of times a 6 comes up be μₐ

   and let the total number of outcomes be n

   using the formula μₐ = nρₐ

   μₐ = 8 * 1/6

        = 1.33

d. let the mean nos of times an odd nos comes up beμₓ

   let the total outcomes be n = 8

   let the probability odd be pb = 1/2

   μₓ = npb

        = 8 * (1/2)

        = 4

e. the standard deviation of a random variable A is given as follows

σₐ

where p = 1/6 (prob 6 outcome)

n = total outcomes = 8

  = 1.0540

f. the standard dev of the binomial random variable Y is given by

σ

where p = 1/2 and n = 8

  =  

  = 1.4142

Here we will show you step-by-step with detailed explanation how to calculate 48 divided by 32 using long division.

Before you continue, note that in the problem 48 divided by 32, the numbers are defined as follows:

48 = dividend

32 = divisor

Step 1:

Start by setting it up with the divisor 32 on the left side and the dividend 48 on the right side like this:

 3 2 ⟌ 4 8  

Step 2:

The divisor (32) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

       0    

 3 2 ⟌ 4 8  

Step 3:

Multiply the divisor by the result in the previous step (32 x 0 = 0) and write that answer below the dividend.

       0    

 3 2 ⟌ 4 8  

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

       0    

 3 2 ⟌ 4 8  

     - 0    

       4    

Step 5:

Move down the 2nd digit of the dividend (8) like this:

       0    

 3 2 ⟌ 4 8  

     - 0    

       4 8  

Step 6:

The divisor (32) goes into the bottom number (48), 1 time(s). Therefore, put 1 on top:

       0 1  

 3 2 ⟌ 4 8  

     - 0    

       4 8  

Step 7:

Multiply the divisor by the result in the previous step (32 x 1 = 32) and write that answer at the bottom:

       0 1  

 3 2 ⟌ 4 8  

     - 0    

       4 8  

      3 2  

Step 8:

Subtract the result in the previous step from the number written above it. (48 - 32 = 16) and write the answer at the bottom.

       0 1  

 3 2 ⟌ 4 8  

     - 0    

       4 8  

     - 3 2  

       1 6  

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 48 divided by 32 calculated using Long Division is:

1

16 Remainder

Answer:

i think it might be C

Step-by-step explanation:

Answer:

8.4

Step-by-step explanation:

Answer:x= 31/6

Step-by-step explanation:

Solve for  

x

by simplifying both sides of the equation, then isolating the variable.