# A new roller coaster at an amuse-6.32Tall enough to ride?TRY ment park requires individuals to be at least 4' 8" (56inches) tall to ride. It is estimated that the heights of10-year-old boys are normally distributed with pinches and o54.54.5 inches.a. What proportion of 10-year-old boys is tall enough toride the coaster?b. A smaller coaster has a height requirement of 50inches to ride. What proportion of 10 year-old-boys istall enough to ride this coaster?c. What proportion of 10-year-old boys is tall enough toride the coaster in part b but not tall enough to ride thecoaster in part a?

Question
Step 1

6.32)

a.

The proportion of 10-year-old boys is tall enough to ride the coaster is 0.3707 and it is calculated below:

From the given information, let us define the random variable X as the heights of 10-year-old boys follows normal distribution with a mean 54.5 inches and standard deviation 4.5 inches. The roller coaster requires individuals to be at least 56 inches.

Step 2

b.

The proportion of 10-year-old boys is tall enough to ride the coaster is 0.8413 and it is calculated below:...

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