Question

The bureau of labor statistics reported in a recent year that’s 16% of US nonfarm workers government employees. A random sample of 50 workers is drawn.

A) is it appropriate to use a normal approximation to find the probability that than 20% of the individuals in the sample are government employees? If so find the probability if not explain why not.

B) A new sample of 90 workers is chosen find the probability that more than 20% of workers in the sample are government employees

C) find the probability that the proportion of workers in the sample of 90 who ate government employees is between .15 and .18

D) find the probability that less than 25% of workers in the sample of 90 are government employees

E) would it be an usual if the portion of government employees in a sample of 90 was greater than .25

Answer 1

Here we have

n=50, p = 0.16

A)

Since np=30 and n(1-p) = 20 are greater than 5 so normal approximation is appropriate.

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

The probability that more than 20% of the individuals in the sample are government employees is

B)

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

The probability that more than 20% of the individuals in the sample are government employees is

C)

The z-score for is

The z-score for is

The probability that the proportion of workers in the sample of 90 who ate government employees is between .15 and .18 is

d)

The z-score for is

The probability that less than 25% of workers in the sample of 90 are government employees is

e)

Since this probability is lesser than 0.05 so it is unusual.