an =A population of values has a normal distribution with y = 218.4 and o = 86.3. A random sample of size167 is drawn. Find the probability that a sample of size n = 167 is randomly selected with a mean

Herodrigues asked Oct 26, 2023

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Herodrigues asked Oct 26, 2023

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10 votes

Given:

$\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4}$

The z-score value is

$z=\frac{M-\mu}{\frac{\sigma}{\sqrt[]{n}}}$

$\text{Substitute }\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4, we get}$

$z=\frac{220.4-218.4}{\frac{86.3}{\sqrt[]{167}}}$

$z=\frac{\sqrt[]{167}(220.4-218.4)}{86.3}$

The P-value from the z-table is

Hence the answer is

Piyush Patil answered Oct 29, 2023

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