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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