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krok68 [10]
3 years ago
8

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard devi

ation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?
Mathematics
1 answer:
alexira [117]3 years ago
3 0

Answer: 0.8490

Step-by-step explanation:

Given :  The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. \mu=30 and \sigma=0.9

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula : z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

P(29.82

∴ Required probability = 0.8490

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