Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149 millimeters, and a standard deviation of 5 millimeters.
If a random sample of 49 steel bolts is selected, what is the probability that the sample mean would be less than 150.4 millimeters? Round your answer to four decimal places.
Solution :
Given that ,
mean =
= 149
standard deviation =
= 5
n = 49
= 149
=
/
n = 5 /
49 = 0.7143
P(
< 150.4) = P((
-
) /
< (150.4 - 149) / 0.7143)
= P(z < 1.96)
= 0.9750
Probability = 0.9750
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