A new roller coaster at an amusement 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 mu equals 53.5 inches and sigma equals 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? a. The proportion of 10-year-old boys tall enough to ride the coaster is 0.3085. (Round to four decimal places as needed.) b. The proportion of 10 year-old-boys tall enough to ride the smaller coaster is 0.7580. (Round to four decimal places as needed.) c. The proportion of 10-year-old boys tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a is nothing. (Round to four decimal places as needed.)

a) The proportion of 10-year-old boys tall enough to ride the coaster is 0.3085

b) The proportion of 10 year-old-boys tall enough to ride the smaller coaster is 0.6925

c) The proportion of 10-year-old boys tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a is 0.3840

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a. What proportion of 10-year-old boys is tall enough to ride the coaster?

Taller than 56 inches, which is 1 subtracted by the pvalue of Z when X = 56.

has a pvalue of 0.6915

1 - 0.6915 = 0.3085

The proportion of 10-year-old boys tall enough to ride the coaster is 0.3085

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?

Taller than 50 inches, which is 1 subtracted by the pvalue of Z when X = 50.

has a pvalue of 0.3075

1 - 0.3075 = 0.6925

The proportion of 10 year-old-boys tall enough to ride the smaller coaster is 0.6925

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?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

X = 56

has a pvalue of 0.6915

X = 50

has a pvalue of 0.3075

0.6915 - 0.3075 = 0.3840

The proportion of 10-year-old boys tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a is 0.3840

sorry, i don't know i just need points, i'm new here. chao

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.