According to survey​ data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a standard deviation of 3.1 inches. a. What percentage of men have arm spans between 66 and 76 ​inches? b. A particular professional basketball player has an arm span of almost 89 inches. Find the​ z-score for this​ person's arm span. What percentage of males have an arm span at least as long as this​ person?

a) 89.97% of men have arm spans between 66 and 76 ​inches.

b) The z-score for this​ person's arm span is 5.68. 0% of males have an arm span at least as long as this​ person

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions 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.

Mean of 71.4 inches and a standard deviation of 3.1 inches.

This means that

a. What percentage of men have arm spans between 66 and 76 ​inches?

The proportion is the pvalue of Z when X = 76 subtracted by the pvalue of Z  when X = 66. The percentage is the proportion multiplied by 100.

X = 76

has a pvalue of 0.9306

X = 66

has a pvalue of 0.0409

0.9306 - 0.0409 = 0.8997

0.8997*100% = 89.97%

89.97% of men have arm spans between 66 and 76 ​inches.

b. A particular professional basketball player has an arm span of almost 89 inches. Find the​ z-score for this​ person's arm span. What percentage of males have an arm span at least as long as this​ person?

The z-score for this​ person's arm span is 5.68.

Z = 5.68 has a pvalue of 1

1 - 1 = 0

0% of males have an arm span at least as long as this​ person

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)