You are the coach of a basketball team that is currently looking for new players. One of the criteria for selection as a player is that the person must be above a particular height. Ideally, you want your next player to be as tall as possible. However, you do not want to rule out any potential players by making the cut-off height too strict. You decide that accepting players within the top 2.5% height bracket will be reasonable for your team. 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. Calculate the cut-off height (C) that ensures only people within the top 2.5% height bracket are allowed into the team. you may find this standard normal table useful. Give your answer in inches to the nearest inch. C= in

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 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.

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

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.

Rounded to the nearest inch,

C = 75 in

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step-by-step explanation: