Question

The ACT is an achievement test given nationally with normally distributed scores. Tim

Answer 1

Answer:

34.83% of the population scored higher than Tim on the mathematics portion of the ACT

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

$Z = \frac{X - \mu}{\sigma}$

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 question, we have that:

$\mu = 22, \sigma = 5.1$

Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?

The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{24 - 22}{5.1}$

$Z = 0.39$

$Z = 0.39$ has a pvalue of 0.6517

1 - 0.6517 = 0.3483

34.83% of the population scored higher than Tim on the mathematics portion of the ACT