A researcher determined that the heights of male students in a
particular town are normally distributed with a mean of 63 inches and
a standard deviation of 1.5. Use the graph above to answer the
following questions:
a. What percentage of these students is taller than 66 inches?
b. If the data are based on 200 students, how many students are
between 60 and 64.5 inches tall? Explain.
a. To find the percentage of students taller than 66 inches, we need to find the z-score first:
z = (x - μ) / σ
z = (66 - 63) / 1.5
z = 2
Looking at a standard normal distribution table or using a calculator, we find that the percentage of students taller than 66 inches is approximately 2.28%.
b. To find the number of students between 60 and 64.5 inches tall, we need to find the z-scores for both heights:
z1 = (60 - 63) / 1.5
z1 = -2
z2 = (64.5 - 63) / 1.5
z2 = 1
Using the standard normal distribution table or calculator, we find the area to the left of z1 is approximately 0.0228 and the area to the left of z2 is approximately 0.8413. To find the number of students between these heights, we subtract the smaller area from the larger area:
0.8413 - 0.0228 = 0.8185
So, approximately 82 students are between 60 and 64.5 inches tall.