Question

The Director of Vehicle Maintenance for a large mass transportation authority wants to know the average life of bus tires for the fleet of 1,800 busses. A random sample of 100 tires is studied and the mean life is 20,000 miles with a standard deviation of 1,200 miles. Construct a 95% confidence interval for the true life of tires.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 20000

Population standard deviation = = 1200

Sample size = n = 100

Z_/2 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (1200 / 100)

= 235

At 95% confidence interval estimate of the population mean is,

- E < < + E

20000 - 235 < < 20000 + 235

19765< < 20235

(19765 , 20235)