The probability calculate the z-score find the probability

Solved Step by Step With Explanation- Probability with Sample Mean

Questions

a. Less than 74.

b. Between 74 and 76.

6. Answer

Let me go through the steps with a bit more detail for each part:

Calculate the standard deviation of the sample mean (σxˉ​):

σxˉ​=$\frac{\sigma}{\sqrt{}n}$

Calculate the z-score:

Z=(74-μxˉ)/​ σx

So, the probability is 0.1038.

b) P(74<xˉ<76)

Z=1.26

Find the probability between these z-scores:

Calculate the z-scores:

Z2=(76-μxˉ)/​ σx

P(1.26<z<2.53)=P(z<2.53)−P(z<1.26)

≈0.9943−0.8962=0.0981

Z=2.53

Find the probability:

b) The probability is 0.7924.

c) The probability is 0.0981.