Problem

The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The team's center is 6.9 feet tall. Find the center's z-score. Is his score unusual? A. 3.83, no B. 4.5 , yes c. 4, no D. 4.95 , yes (1) Time Remaining: 01:39:07 Next Search

Solution

Step 1 :Define the given values: mean height of the team (\(\mu\)) is 6 feet, standard deviation (\(\sigma\)) is 0.2 feet, and the center's height (\(X\)) is 6.9 feet.

Step 2 :Calculate the z-score using the formula: \(Z = \frac{X - \mu}{\sigma}\)

Step 3 :Substitute the given values into the formula: \(Z = \frac{6.9 - 6}{0.2} = 4.5\)

Step 4 :In a normal distribution, about 99.7% of the data falls within 3 standard deviations of the mean. Therefore, a z-score of 4.5 is unusual because it is more than 3 standard deviations away from the mean.

Step 5 :Final Answer: \(\boxed{B. 4.5 , yes}\)

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Source: https://solvelyapp.com/problems/20737/

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