In a certain year, 26% 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 3,000 teenagers, what number of teenagers without checking accounts can it expect to find? _2220_ 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.)

(a) To find the number of teenagers without checking accounts that TeenChex can expect to find, we need to multiply the percentage of teenagers without checking accounts by the sample size.

Given that 26% of all teenagers in the United States have checking accounts, it means that 100% - 26% = 74% of teenagers do not have checking accounts.

So, the expected number of teenagers without checking accounts in the sample is:

Expected number = (Percentage without checking accounts) x (Sample size)
= 0.74 x 3000
= 2220

Therefore, TeenChex can expect to find 2220 teenagers without checking accounts in the sample.

(b) To find the standard deviation (σ) of the number of teenagers without checking accounts, we can use the formula for the standard deviation of a binomial distribution:

Standard deviation (σ) = sqrt(n * p * (1 - p))

where "n" is the sample size and "p" is the percentage of teenagers without checking accounts.

Plugging in the values, we have:

σ = sqrt(3000 * 0.74 * (1 - 0.74))
= sqrt(2220 * 0.74)
≈ sqrt(1642.8)
≈ 40.6

So, the standard deviation (σ) of the number of teenagers without checking accounts is approximately 40.6.

For the missing quantities, we need to find the range of the number of teenagers without checking accounts that falls within the 95% confidence interval. To do this, we can use the concept of the normal distribution.

Given a normal distribution, approximately 95% of the data falls within two standard deviations (plus or minus) of the mean.

So, we can calculate the 95% confidence interval as follows:

Lower bound = Expected number - (2 * σ)
Upper bound = Expected number + (2 * σ)

Lower bound = 2220 - (2 * 40.6)
Upper bound = 2220 + (2 * 40.6)

Lower bound ≈ 2139
Upper bound ≈ 2301

Therefore, there is an approximately 95% chance that between 2139 and 2301 teenagers in the sample will not have checking accounts.