Question

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 2.2 gallons. From his records, he selects a random sample of 64 sales and finds the mean number of gallons sold is 8.17. (Round your answers to 2 decimal places.)


(a) The point estimate of the population mean is

I know the answer to this is 8.17


(b) The 99 percent confidence interval for the population mean is between and .

Answer 1

Answer with explanation:

As per given , we have

$\ovreline{x}=8.17$

$\sigma=2.2$

n= 64

a) Since , the sample mean is the point estimate for the population mean.

Therefore, the point estimate of the population mean =$\ovreline{x}=8.17$

b) Critical z-value for 99% confidence : $z_{\alpha/2}=2.576$

Confidence interval :

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$8.17\pm (2.576)\dfrac{2.2}{\sqrt{64}}$

$8.17\pm 0.7084$

$(8.17-0.7084,\ 8.17+0.7084)=(7.4616,\ 8.8784)\approx (7.46,\ 8.88)$

Hence, the 99 percent confidence interval for the population mean is between 7.46 and 8.88.