In: Statistics and Probability
A company makes batteries that have life spans with a mean of 3000 hours and standard deviation of 70 hours. Find the probability that the mean life span of a random sample of 85 batteries will be over 3020 hours.
Solution :
Given that,
mean =
= 3000
standard deviation =
= 70
n=85
=
=3000
=
/
n = 70/
85 = 7.59
P( > 3020) = 1 - P(
< 3020)
= 1 - P[(
-
) /
< (3020 - 3000) /7.59 ]
= 1 - P(z < 2.64)
Using z table
= 1 - 0.9959
probability=0.0041