PROBLEM # 12

The manager of gas station would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume the number of litres sold follows the normal distribution with a standard deviation of 40 L. From his records, he selects a random sample of 29 sales and finds the mean number of litres sold is 89.

Use these tables to determine thez-value(s) or t-value(s).

(Round z-values to 2 decimals and t-values to 3 decimals)

a. What is the point estimate of the population mean?

The point estimate of the population mean is litres.(Round it to the nearest whole number.)

b. Explain what distribution you will use and why.

(Click to select) z distribution because the population standard deviation is known. t distribution because the population standard deviation is unknown. z distribution because the sample mean is known. t distribution because the sample mean is unknown. z distribution because the the confidence interval is for a population proportion. t distribution because the the confidence interval is for a population proportion.

c. For a 98% confidence interval, what is the value zort(depending on your answer in b.)?

The value ofzortis .

d. Develop a 98% confidence interval for the population mean.

The 98% confidence interval for the population mean is between and .(Round each to 3 decimal places.)

e.Interpret the meaning of part (d).

If 100 such intervals were determined, the (Click to select) sample mean population variance sample statistic population mean sample variance would appear in about of those intervals.