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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
A new roller coaster at an amuse-
6.32
Tall enough to ride?
TRY ment park requires individuals to be at least 4' 8" (56
inches) tall to ride. It is estimated that the heights of
10-year-old boys are normally distributed with p
inches and o
54.5
4.5 inches.
a. What proportion of 10-year-old boys is tall enough to
ride the coaster?
b. A smaller coaster has a height requirement of 50
inches to ride. What proportion of 10 year-old-boys is
tall enough to ride this coaster?
c. What proportion of 10-year-old boys is tall enough to
ride the coaster in part b but not tall enough to ride the
coaster in part a?
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A new roller coaster at an amuse- 6.32 Tall enough to ride? TRY ment park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated that the heights of 10-year-old boys are normally distributed with p inches and o 54.5 4.5 inches. a. What proportion of 10-year-old boys is tall enough to ride the coaster? b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10 year-old-boys is tall enough to ride this coaster? c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?

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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.

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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:...

P(X250)= PX= u50-u
50 54.5
4.5
- P(z 2-1)
From standard normal table,
-1-P(z<-1)
P(z<-1) 0.1587
=1-0.1587
=0.8413
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P(X250)= PX= u50-u 50 54.5 4.5 - P(z 2-1) From standard normal table, -1-P(z<-1) P(z<-1) 0.1587 =1-0.1587 =0.8413

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