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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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
[tex]\mu = 70, \sigma = 2.7[/tex]
What percentage of the business travelers will have to stoop?
This is 1 subtracted by the pvalue of Z when X = 69. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 70}{2.7}[/tex]
[tex]Z = -0.37[/tex]
[tex]Z = -0.37[/tex] has a pvalue of 0.3557.
1 - 0.3557 = 0.6443
0.6443 = 64.43% of the business travelers will have to stoop
