Question

You spin a wheel of fortune that is equally likely to end up pointing to any decimal number between 0 and 1, and you win if it points to a number between 0.50 and 0.55. If you spin this wheel 100 times, the mean and standard deviation of the number of times you win are closest to which of the following?

a. 5.0 and 2.18, respectively
b. 10.0 and 3.0, respectively
c. 5.0 and 4.75, respectively
d. You can’t tell because the result of a single spin is not normally distributed

Answer 1

a. 5.0 and 2.18, respectively

Explanation:

n = numbers of spins = 100 times

p = 0.55 - 0.50 = 0.05

q = 1 - 0.05 = 0.95

Mean = n x p = 100 x 0.05 = 5

Standard Deviation =
`√(npq)`

Standard Deviation =
`√(100 X 0.05 X 0.95)`

Standard Deviation =
`√(4.75)`

Standard Deviation = 2.1794

Standard Deviation = 2.18