Question

Test scores on a statewide standardized test for a large population of students are normally distributed with mean = 9.44 and standard deviation = 1.75. certificates are given to students who score in the top 2.5% of those who took the test. fred, a student who took the test, finds out that he earned a score of 13.1 on the test. he will not get a certificate

Answer 1

True, he will not get the certificate.

Explanation:

Answer 2

Since about 95% of a normal distribution falls within two standard deviations of the mean
`\bigg(\mathbb P(-2<Z<2)\approx0.95\bigg)`, it follows that 5% lie outside this range, with 2.5% lying to either side of it.This means
`\mathbb P(Z<2)=0.975=97.5\%`, with the remaining 2.5% lying above
`Z=2`.

This means for a score to belong in the top 2.5%, it's corresponding z-score must be higher than 2.

Fred scores 13.1 on the test. The corresponding z-score is


`z=(13.1-9.44)/(1.75)\approx2.0914`

which is barely higher than 2, but high enough to earn that certificate.