Question

A researcher determined that the heights of male students in a particular town are normally distributed with a mean of 65 inches and a standard deviation of 1.7. Use the graph above to answer the following questions:

a. What percentage of these students is taller than 66.7 inches?

b. If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall? Explain.

Answer 1

a. To find the percentage of students taller than 66.7 inches, we first need to calculate the z-score for this height:

z = (x - μ) / σ
z = (66.7 - 65) / 1.7
z = 1.7 / 1.7
z = 1

Using the standard normal distribution table or a calculator, we can find that the percentage of students taller than 66.7 inches (z-score of 1) is approximately 15.87%.

b. To find the number of students between 61.6 and 68.4 inches tall out of 300 students, we need to find the z-scores for both heights:

For 61.6 inches:
z = (61.6 - 65) / 1.7
z = -3.4 / 1.7
z = -2

For 68.4 inches:
z = (68.4 - 65) / 1.7
z = 3.4 / 1.7
z = 2

Using a standard normal distribution table or calculator, we can find that the area between z-scores of -2 and 2 is approximately 95.45%.

Out of 300 students, the number of students between 61.6 and 68.4 inches tall would be:
95.45% * 300 = 286.35

Therefore, approximately 286 students are between 61.6 and 68.4 inches tall.