need help with part d and e In 2016, the Better Business Bureau settled 82% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.82, the same as the overall proportion of complaints settled in 2016. Use the z-table.a. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of \(\bar{p}\).- \(E(\bar{p}) =\) ______ (to 2 decimals)- \(\sigma_{\bar{p}} =\) ______ (to 4 decimals)b. Based upon a sample of 200 complaints, what is the probability that the sample proportion will be within 0.06 of the population proportion (to 4 decimals)?- Probability = ______c. Suppose you select a sample of 440 complaints involving new car dealers. Show the sampling distribution of \(\bar{p}\).- \(E(\bar{p}) =\) ______ (to 2 decimals)- \(\sigma_{\bar{p}} =\) ______ (to 4 decimals)d. Based upon the larger sample of 440 complaints, what is the probability that the sample proportion will be within 0.06 of the population proportion (to 4 decimals)?- Probability = ______e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (d)?The probability of the sample proportion being within 0.06 of the population mean is increased by ______ (to 3 decimals). There is a gain in precision by ______ the sample size.

From the information, given that Let the random variable X follows binomial distribution with The value for np and nq are both greater than 10, that is both the conditions are satisfied. Since both conditions are satisfied, this implies that normal approximation is appropriate.(d)The probability that the sample proportion will be within 0.06 of the population proportion for the sample of size of 440 complaints is obtained as follows: The mean of the sampling distribution of the sample proportion is,The required probability is,The probability that the sample proportion will be within 0.06 of the population proportion for the sample of size of 440 complaints is 0.9990.(e)The value of gain in precision is determined as follows: The probability that the sample proportion will be within 0.06 of the population proportion for the sample of size of 200 complaints is,That is, the value of gain is 0.0262(=0.999–0.9728). The probability of the sample proportion being within 0.06 of the population mean is increases by 0.026.. There is a gain in precision by increasing the sample size. (d)The probability that the sample proportion will be within 0.06 of the population proportion for the sample of size of 440 complaints is 0.9990.(e)The probability of the sample proportion being within 0.06 of the population mean is increases by 0.026.. There is a gain in precision by increasing the sample size.