Bob Nale is the owner of Nale$$s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of $2\mathrm{.}50$ gallons. From his records, he selects a random sample of $55$ sales and finds the mean number of gallons sold is $5\mathrm{.}40.($Use t Distribution Table & z Distribution Table.$)$

Required:

What is the point estimate of the population mean?

Note: Round your answer to $2$ decimal places.

Develop a $90\%$ confidence interval for the population mean.

Note: Round z$-$score and your answers to $2$ decimal places.