Question

The cabin of a business jet has a cabin height 5 feet 9 inches high. If a business traveler’s height is N(5'10", 2.7"), what percentage of the business travelers will have to stoop? (Round your answer to 4 decimal places.) Probability

Answer 1

Answer:

0.6443 = 64.43% of the business travelers will have to stoop

Step-by-step explanation:

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

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

$Z = \frac{X - \mu}{\sigma}$

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:

Each feet is 12 inches

So

5'9'' = 5*12 + 9 = 69

5'10'' = 5*12 + 10 = 70

$\mu = 70, \sigma = 2.7$

What percentage of the business travelers will have to stoop?

This is 1 subtracted by the pvalue of Z when X = 69. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{69 - 70}{2.7}$

$Z = -0.37$

$Z = -0.37$ has a pvalue of 0.3557.

1 - 0.3557 = 0.6443

0.6443 = 64.43% of the business travelers will have to stoop