Posted by Sophie on .
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. 35,40236,998
b. 31,83040,570
c. 35,43636,964
d. 35,36737,033
Is it C?

Math 
PsyDAG,
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.