Question

A study was done to determine the stress levels that students have while taking exams. The stress level was found to be normally distributed with a mean stress level of 8.2 and a standard deviation of 1.34. What is the probability that at your next exam, you will have a stress level between 9 and 10?

Answer 1

Answer: 0.1841

Explanation:

Given: Mean :
`\mu=8.2`

Standard deviation :
`\sigma = 1.34`

The formula to calculate z-score is given by :_

`z=(x-\mu)/(\sigma)`

For x= 9, we have

`z=(9-8.2)/(1.34)\approx0.60`

For x= 10, we have

`z=(10-8.2)/(1.34)\approx1.34`

The P-value =
`P(0.6<z<1.34)=P(z<1.34)-P(z<0.6)`

`=0.9098773-0.7257469=0.1841304\approx0.1841`

Hence, the probability that at your next exam, you will have a stress level between 9 and 10 = 0.1841