In a simple random sample of 150 households, the sample mean number of personal computers was 1.32. Assume the population standard deviation is σ = 0.41.

a. Construct a 95% confidence interval for the mean number of personal computers.

b. If the sample size were 100 rather than 150, would the margin of error be larger or smaller than the result in part (a)? Explain.

c. If the confidence level were 98% rather than 95%, would the margin of error be larger or smaller than the result in part (a)? Explain.

d. Based on the confidence interval constructed in part (a), is it likely that the mean number of personal computers is greater than 1.25?