Question

Suppose that scores on a particular test are normally distributed with a mean of and a standard deviation of . What is the minimum score needed to be in the top of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.

Answer 1

Answer:

The minimum score needed to be in the top 5% of the scores on the test is 172.9.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the minimum score needed to be in the top 5% of the scores on the test?

The 100-5 = 95th percentile, which is the value of X when Z has a pvalue of 0.95. So it is X when Z = 1.645.

The minimum score needed to be in the top 5% of the scores on the test is 172.9.