A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6)outcomes?
A)18
B)9
C)5
D)3
E)1.732

Question

Quizplus · Accepted Answer

The probability of rolling an even number on a fair die is 1/2. Therefore, the expected value of the number of even outcomes in 36 rolls is (1/2) * 36 = 18.

To calculate the standard deviation of the even outcomes, we need to use the formula:

SD = sqrt [ Σ(x - μ)^2 / N ]

where: 
- x is the number of even outcomes (2, 4, or 6) 
- μ is the mean of the even outcomes, which is 18 
- N is the number of rolls, which is 36

Let's fill in the formula:

SD = sqrt [ ( (2-18)^2 + (4-18)^2 + (6-18)^2 ) / 36 ]

= sqrt [ ( 16 + 196 + 256 ) / 36 ]

= sqrt [ 24 ]

= 4.899

Rounding this to the nearest whole number gives us a standard deviation of 5. Therefore, the answer is D.

A Fair Die Is Rolled 36 Times