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sveta [45]
2 years ago
11

An anthropologist wishes to estimate the average height of men for a certain race of people. If the population standard deviatio

n is assumed to be 2.8 inches and if she randomly samples 100 men, find the probability that the difference between the sample mean and the true population mean will not exceed 0.7 inch. (Round your answer to four decimal places.)
Mathematics
1 answer:
mario62 [17]2 years ago
5 0

Answer:

The probability that the difference between the sample mean \bar{x} and the true population mean \mu is : P[|\bar{x}-\mu|\leq0.7]=0.9876

Step-by-step explanation:

Given :

Population standard deviation \sigma=2.8.

Sample size n=100

The sample mean standard deviation=\frac{\sigma}{\sqrt{n}}

To find :

The probability that the difference between the sample mean \bar{x} and the true population mean \mu

\because\frac{\sigma}{\sqrt{n}}=\frac{2.8}{\sqrt{100}}=\frac{2.8}{10}=0.28

Now, the probability that the difference between the sample mean \bar{x} and the true population mean \mu is :

  P[|\bar{x}-\mu|\leq0.7], nis large \Rightarrow \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=z

\Rightarrow P[\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}

\Rightarrow P[z

\Rightarrow P[-2.5

Therefore, the probability P[|\bar{x}-\mu|\leq0.7]=0.9876

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