Answer:
C = 75 in
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be 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.
Assume that the height of all people follows a normal distribution with a mean of 69 in and a standard deviation of 2.9 in.
This means that [tex]\mu = 69, \sigma = 2.9[/tex]
Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team.
This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 69}{2.9}[/tex]
[tex]X - 69 = 1.96*2.9[/tex]
[tex]X = 74.7[/tex]
Rounded to the nearest inch,
C = 75 in