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.

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

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

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

Answer 1

The number of US adults who thing that pennies should still be made could be modelled here as:

a) The expected number of adults who continue making pennies is computed here as:
E(X) = np = 20*0.76 = 15.2
Therefore 15.2 is the expected number of adults expected to indicate that they should continue making pennies.

The standard deviation here is computed as:

Therefore 1.91 is the required standard deviation here.

b) The likelihood that exactly 8 people would indicate the Treasury should continue making pennies is computed using the binomial probability function as: (EXCEL Function)

=binom.dist(8,20,0.76,FALSE)

0.000512 is the required probability here.

c) The probability that 10 to 15 adults would indicate the Treasury should continue making pennies is computed using the cumulative binomial probability function in EXCEL as:

=binom.dist(15,20,0.76,TRUE)-binom.dist(9,20,0.76,TRUE)

Therefore 0.541144 is the required probability here.