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

The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

What is a normal distribution?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of 65 inches and a standard deviation of 1.7.

From the graph:

P(X> 66.7) = (13.5 + 2.35 + 0.15)%

P(X> 66.7) = 16%

P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)%  = 95%

= (300×95)/100

= 285 students

Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

Learn more about the normal distribution here:

brainly.com/question/12421652

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