# Working with sampling distribution and probability.

A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

b) Find P(p^ >= 0.05)

c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:42 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/working-with-sampling-distribution-and-probability-6692

#### Solution Preview

a) If the true unemployment rate is 6%, then let X be the number of people who were unemployed. Obviously,

X~b(700,0.06), that is a binomial distribution with n=700, and p=0.06. So p^=(X1+X2+...+X700)/700 approximately follows normal distribution, where

<br> E(p^)={E(X1)+E(X2)+...+E(X700)}/700=0.06,

<br>and

<br> ...

#### Solution Summary

A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

b) Find P(p^ >= 0.05)

c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.