Question

About 6% of employed adults in the United States held multiple jobs. A random sample of 69 employed adults is chosen. Use the TI-84 Plus calculator as needed. Part 1 of 5 (a) Is it appropriate to use the normal approximation to find the probability that less than 6.6% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not. It is appropriate to use the normal curve, since np - 4.14 10. < Part: 1/5 Part 2 of 5 (b) A new sample of 339 employed adults is chosen. Find the probability that less than 6.6% of the individuals in this sample hold multiple jobs. Round the answer to at least four decimal places. The probability that less than 6.6% of the individuals in this sample hold multiple jobs is II Х

Answer 1

Solution:-

a) It is not appropriate ti use the normal curve, since np = 4.14 is less than 10.

b) The probability that less than 6.6% of the individuals in the sample hold multiple jobs is 0.6791.

p = 0.066

By applying normal distribution:-

$z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$z= \frac{0.066-0.06}{\sqrt{\frac{0.06(1-0.06)}{339}}}$

z = 0.4652

P(z < 0.4652) = 0.6791