Question

The exam scores on a statistics final exam are normally distributed with a mean of 140 points out of 200 and standard deviation of 8. What is the probability that a randomly selected student scored less than 156 on the final exam

Answer 1

Answer:0.78%

Step-by-step explanation:

Answer 2

Answer:

Probability that a randomly selected student scored less than 156 on the final exam is 0.97725 .

Step-by-step explanation:

We are given that the exam scores on a statistics final exam are normally distributed with a mean of 140 points out of 200 and standard deviation of 8.

Let X = Score of students in exam

So, X ~ N($\mu = 140, \sigma^{2} =8^{2}$)

The z score probability distribution is given by;

           Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 140

            $\sigma$ = standard deviation = 8

So, the probability that a randomly selected student scored less than 156 on the final exam is given by = P(X < 156)

 P(X < 156) = P( $\frac{X-\mu}{\sigma}$ < $\frac{156-140}{8}$ ) = P(Z < 2) = 0.97725 .

Therefore, the probability that a randomly selected student scored less than 156 on the final exam is 0.97725 .