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Nuetrik [128]
3 years ago
6

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 142 millimeters,

and a standard deviation of 6 millimeters. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would be greater than 139.7 millimeters? Round your answer to four decimal places.
Mathematics
1 answer:
eimsori [14]3 years ago
7 0

Answer: 0.9884

Step-by-step explanation:

Given :  Population mean : \mu=142

and standard deviation : \sigma=6

sample size : n= 35

Let x be the random variable that represents the diameter of steel bolts.

Using formula z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}} ,

The z-value corresponds to x=139.7

z=\dfrac{139.7-142}{\dfrac{6}{\sqrt{35}}}\approx-2.27

The probability that the sample mean would be greater than 139.7 millimeters will be :-

P(x>139.7)=P(z>-2.27)=1-P(z

Hence, the required probability : = 0.9884

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