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.
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.
1 answer