The freshness of produce at a mega-store is rated a scale of 1 to 5 , with 5 being very fresh. From a random sample of 36 customers, the average score was 3.5 with a standard deviation of 0.8.

(a) Obtain a \(90 \%\) confidence interval for the population mean, \(\mu\), or the mean score for all customers.

(b) Does \(\mu\) lie in your interval obtained in part (a)? Explain.

(c) In long series of repeated experiments, with new random samples collected for each experiment, what proportion of the resulting confidence intervals will contain the true population mean? Explain your reasoning.