Question

About 7% of employed adults in the United States held multiple jobs. A random sample of 71 employed adults is chosen. Use the TI-84 Plus calculator as needed.

(a) Is it appropriate to use the normal approximation to find the probability that less than 5.4% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not.

Answer 1

To check whether it is appropriate or not to use the normal approximation to find the probability that less than 5.4% of the individuals in the sample hold multiple jobs, we need to first check the sample size conditions which are given below

and , both must be greater than 10. If these conditions are satisfiefd, then only we can use the normal approximation.

we have n = 71 and p = 7% = 7/100 = 0.07

So, we get

So, it is clear that only one condition is satisfied. Thus, we can say that it is not appropriate to use normal approximation to find the probabilty because conditions are not satisfied.