Question

In a random sample of 30 tires of the same type, it is found that the average life span is 36,200 miles with a standard deviation of 3800 miles.

Find the interval about the sample mean such that the probability is 0.77 that the mean number lies within the interval.
a. 35,402-36,998
b. 31,830-40,570
c. 35,436-36,964
d. 35,367-37,033

Is it C?

Answer 1

You are looking for the proportion that lie in the area μ ± .385 = μ ± 1.2 SD. (This information is available from a table in the back of your stats text called something like "areas under the normal distribution.")

However, for a distribution of means, you need the standard error rather than the standard deviation.

SE = SD/sq rt of n

So you are looking for μ ± 1.2SE

You should be able to calculate the values from this.

I hope this helps. Thanks for asking.