Question

10. The scores on the verbal section of the Graduate Records Examination (GRE)

are approximately normally distributed with a mean of 150 and a standard
deviation of 8.5. What is the probability that a randomly selected score on the
verbal section is higher than 1657

Answer 1

The probability that a randomly selected score on the verbal section is higher than 165 is 0.0392

Explanation:

We are given that The scores on the verbal section of the Graduate Records Examination (GRE) are approximately normally distributed with a mean of 150 and a standard deviation of 8.5.

Mean =
`\mu = 150`

Standard deviation =
`\sigma = 8.5`

We are supposed to find the probability that a randomly selected score on the verbal section is higher than 165 i.e.P(x>165)

Formula :
`Z=(x-\mu)/(\sigma)`

`Z=(165-150)/(8.5)`

Z=1.76

Refer the z table for p value

P(x<165)=0.9608

P(x>165)=1-P(x<165)=1-0.9608=0.0392

Hence the probability that a randomly selected score on the verbal section is higher than 165 is 0.0392