Test scores for a standardized math test follow a normal distribution with a mea

Question

Test scores for a standardized math test follow a normal distribution with a mean of 73 and a standard deviation of 8. A random sample of 23 students took this math test. What is the probability that the average score of the 23 students falls above 75?

10. Test scores for a standardized math test follow a normal distribution with a mean of 73 and a standard deviation of 8. A random sample of 23 students took this math test. What is the probability that the average score of the 23 students falls above 75?

Explanation / Answer

Solution:

Given that, = 73, = 8 and n = 23

Let x be the average score of the students.

Now, P(x 75) = 1 – P (x 75)

                        = 1 – P [z {(75 – ) } //n}]

                       = 1 – [P (75 – 73)/8/23]

                       = 1 – P(z 1.7964)

Since using normal distribution table, we get

P(x 75) = 1 – 0.8849

               = 0.1151

Therefore, the probability that the average score of the 23 students fall above 75 is 0.1151.

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