Question

You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is ?¯=50 months. Suppose that the lifetimes for tires of this brand follow a Normal distribution, with unknown mean ? and standard deviation ?=5 months, then a 99% confidence interval for ? is: A) 48.78 to 51.22. B) 49.8 to 50.2. C) 40.2 to 59.8. D) 48.39 to 51.61.

Answer 1

Answer:

D) 48.39 to 51.61.

Explanation:

Here we use the following formula to find the confidence interval.

Here we have n = 64 ( number of tires), sample mean is ?¯=50 months and  standard deviation ?=5 months.

We have 99% confidence so alpha = 0.01. We can find from normal distribution table

from table.

So, 99% confidence interval from above formula is

=( 48.39375 , 51.60625 )

= ( 48.39, 51.61 ) ... rounded to 2 decimals

Hence option D is correct.

99% confidence interval for ? is 48.39 to 51.61.

## MINITAB output for reference:

One-Sample Z

The assumed standard deviation = 5

N Mean SE Mean 99% CI
64 50.000 0.625 (48.390, 51.610)

Other options are wrong.