A manufacturer knows that their items have a normally
distributed lifespan, with a mean of 5 years, and standard
deviation of 0.7 years.
If 20 items are picked at random, 6% of the time their mean life
will be less than how many years?
Give your answer to one decimal place.
Solution :
Given that,
mean =
= 5
standard deviation =
= 0.7
Sample size = n = 20
=
/
n = 0.7 /
20 = 0.1565
Using standard normal table ,
P(Z < z) = 6%
P(Z < z) = 0.06
P(Z < -1.56) = 0.06
z = -1.56
Using z-score formula,
x = z *
+
x = -1.56 * 0.1565 + 5 = 4.8
6% of the time their mean life will be less than is 4.8 years
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