Acme Inc. is studying the average distance their employees travel to work. This is estimated to be normally distributed. A random sample of 10 employees was taken and revealed the following distances travelled to work (km):

26 42 64 12 57 45 20 36 47 35

At the 95% level of confidence, what is the range of distance (km, in 2 decimal places) traveled to work by the Acme employees?

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

Round all z-values to 2 decimal placesand t-values to 3 decimal places.

Do not round intermediate results or, if you do, round them to 5 decimals.

a. What is the value of the population parameter?

(Click to select) It is unknown. 53.00 38 (1 point)

b. What is the best estimate of this value?Round the answer to 1 decimal place.

(1 point)

c. What distribution should be applied in this case?

(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. (2 points)

d. For the 95% confidence interval, what is the value of z to t (depending on your answer in c.)?

The value of z or t is . (2 points)

e.What is the margin of error for this confidence interval?Round theanswer to 5 decimal places.

Themargin of error is .(2 points)

f. Develop the 95% confidence interval for the distance traveled to work. Round the answers to 2 decimal places.

The 95% confidence interval for the distance travelled to work is from to (km). (1 point each)

g. Would it be reasonable to conclude that the population mean is 53 km?

(Click to select) No Yes (1 point)