Question

A recent CNN News survey reported that 76% of adults think the U.S. pennies should still be made.

Suppose we select a sample of 20 people.

How many of the 20 would you expect to indicate that the Treasury should continue making pennies? What is the standard deviation?

What is the likelihood that exactly eight people would indicate the Treasury should continue making pennies?

What is the likelihood that 10 to 15 adults would indicate the Treasury should continue making pennies?

Answer 1

P(an adult thinks the U.S. pennies should still be made), p = 0.76

Sample size, n = 20

q = 1 - p = 0.24

P(X) = nCx p^x q^n-x

Mean = np

= 20 x 0.76

= 15.2

Standard deviation =

=

= 1.91

P(exactly eight people would indicate the Treasury should continue making pennies) = P(X = 8)

= 20C8 x 0.76⁸ x 0.24¹²

= 0.000512

P(10 to 15 adults would indicate the Treasury should continue making pennies) = P(10) + P(11) + P(12) + P(13) + P(14)

= 20C10x0.76¹⁰x0.24¹⁰ + 20C11x0.76¹¹x0.24⁹ + 20C12x0.76¹²x0.24⁸ + 20C13x0.76¹³x0.24⁷ + 20C14x0.76¹⁴x0.24⁶ + 20C15x0.76¹⁵x0.24⁵

= 0.00753 + 0.02168 + 0.05149 + 0.10034 + 0.15887 + 0.20124

= 0.54115