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

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()

The z score probability distribution is given by;

           Z = ~ N(0,1)

where, = population mean = 140

            = 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( < ) = P(Z < 2) = 0.97725 .

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

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