Question

According to the National Testing Service, last year's ACT college entrance exam scores followed a normal distribution with a mean of 20.8 and a standard deviation of 4.8. A student from that testing group is randomly selected. Find the probability that the person's score was:

a) less than 18

b) between 25 and 30

c) more than 28

Answer 1

To find the probabilities of different ACT scores, we can calculate the corresponding z-scores and use a z-score table or calculator.

Step-by-step explanation:

In order to find the probability that the person's score was less than 18, we need to calculate the z-score for 18 using the formula:

z = (x - mean) / standard deviation

Substituting the given values, we get z = (18 - 20.8) / 4.8 = -0.583. Using a standard normal distribution table or a statistical calculator, we find that the probability is approximately 0.280.

To find the probability that the person's score was between 25 and 30, we again need to calculate the z-scores for both values.

The z-score for 25 is (25 - 20.8) / 4.8 = 0.875, and the z-score for 30 is (30 - 20.8) / 4.8 = 1.938.

From the z-score table or calculator, we find that the probability of a z-score between 0.875 and 1.938 is approximately 0.231.

Finally, to find the probability that the person's score was more than 28, we calculate the z-score for 28: (28 - 20.8) / 4.8 = 1.458.

Again, consulting the z-score table or calculator, we find that the probability is approximately 0.072.