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

Step-by-step explanation:

Given: Mean : $\mu=8.2$

Standard deviation : $\sigma = 1.34$

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

$z=\dfrac{x-\mu}{\sigma}$

For x= 9, we have

$z=\dfrac{9-8.2}{1.34}\approx0.60$

For x= 10, we have

$z=\dfrac{10-8.2}{1.34}\approx1.34$

The P-value = $P(0.6$

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

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