Question

In a certain year, 29% of all teenagers in the United States had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account.

(a) If TeenChex selects a random sample of 2,000 teenagers, what number of teenagers without checking accounts can it expect to find?
teenagers

What is the standard deviation σ of this number? (Round the standard deviation to one decimal place.)
σ =  

(b) Fill in the missing quantities.

There is an approximately 95% chance that between  and  teenagers in the sample will not have checking accounts. (Round answers to the nearest whole number.)

Answer 1

P(Without checking account) = 1 - 0.29 = 0.71

a)

Expected number = n p

= 2000 * 0.71

= 1420

b)

Standard deviation = Sqrt ( np( 1 -p)

= sqrt ( 2000 * 0.71 * 0.29)

= 20.3

c)

According to empirical rule, approximately 95% of the data falls in 2 standard deviation of the mean.

That is between mean - 2 SD and mean + 2 SD

= between 1420 - 2 * 20.3 and 1420 + 2 * 20.3

= between 1397.4 and 1460.6

There is an approximately 95% chance that between 1397 and 1461 teenagers in the sample

will not have checking accounts.