Question

1. A recent CBS News survey reported that 67% of adults felt the US Treasury should continue making pennies. Suppose we select a sample of 15 adults.

1. On average, how many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation?
2. What is the probability that exactly 9 adults would indicate the Treasury should continue making pennies?

Answer 1

Solution :

Given that ,

Using binomial probability formula ,

n = 15

p = 0.67

q = 1 - p = 1 -0.67 = 0.33  

a ) = n * p

= 15 *0.67

= 10.05

Mean = 10

=  n * p * q

= 15 * 0.67 * 0.33

= 1.8211

= 1.35

The standard deviation = 1.35

b ) X = 9

P(X = x) = ((n! / (n - x)!) * px * (1 - p)n - x

P(X = 9) = ((15! / (15 - 9)!) * 0.679 * 0.3315 - 9

= 0.1758

Probability = 0.1758