Question
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A normal distribution curve is shown and labeled. The mean is 65 and the standard deviation is 1.7.
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:
What percentage of these students is taller than 66.7 inches?
If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall? Explain.
A normal distribution curve is shown and labeled. The mean is 65 and the standard deviation is 1.7.
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:
What percentage of these students is taller than 66.7 inches?
If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall? Explain.
Answers
Answered by
GPT 3.5
To find the percentage of students taller than 66.7 inches, we need to find the z-score for 66.7 using the formula:
z = (x - μ) / σ
z = (66.7 - 65) / 1.7
z = 1.7 / 1.7
z = 1
Using a z-table, we find that the percentage of students taller than 66.7 inches is 0.1587, or 15.87%.
Next, 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 these two heights:
z1 = (61.6 - 65) / 1.7 = -2
z2 = (68.4 - 65) / 1.7 = 2
Using a z-table, we find that the area to the left of z1 is 0.0228 and the area to the left of z2 is 0.9772. To find the area between z1 and z2, we subtract these two values: 0.9772 - 0.0228 = 0.9544.
Multiplying this probability by the total number of students (300), we find:
0.9544 * 300 = 286.32
Therefore, approximately 286 students are between 61.6 and 68.4 inches tall.
z = (x - μ) / σ
z = (66.7 - 65) / 1.7
z = 1.7 / 1.7
z = 1
Using a z-table, we find that the percentage of students taller than 66.7 inches is 0.1587, or 15.87%.
Next, 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 these two heights:
z1 = (61.6 - 65) / 1.7 = -2
z2 = (68.4 - 65) / 1.7 = 2
Using a z-table, we find that the area to the left of z1 is 0.0228 and the area to the left of z2 is 0.9772. To find the area between z1 and z2, we subtract these two values: 0.9772 - 0.0228 = 0.9544.
Multiplying this probability by the total number of students (300), we find:
0.9544 * 300 = 286.32
Therefore, approximately 286 students are between 61.6 and 68.4 inches tall.