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Answer :
Final answer:
To find the percentage of heights in a given range, we need to calculate the Z-scores for the given heights and find the corresponding areas under the Normal distribution curve. Using a Z-score table or calculator, we can determine the percentage of heights that fall within specific ranges. For part d, we can multiply the percentage by the total number of players in the sample to find the number of players in a specific height range.
Explanation:
The distribution of heights of kindergarten students is Normal, with a mean of 38.2 inches and a standard deviation of 1.8 inches. To find the percentage of heights in a specific range, we need to calculate the area under the Normal distribution curve between the given heights. This can be done using a Z-score table or a calculator.
a. To find the percentage of heights that are from 67.95 to 71.95 inches, we need to calculate the Z-scores for both heights and find the area between those Z-scores. The Z-score for 67.95 inches is (67.95 - 38.2) / 1.8 = 16.53, and the Z-score for 71.95 inches is (71.95 - 38.2) / 1.8 = 18.86. Using a Z-score table or calculator, we can find the area between these Z-scores, which represents the percentage of heights in that range.
b. To find the percentage of heights that are from 67.95 to 73.95 inches, we need to calculate the Z-scores for both heights and find the area between those Z-scores. The Z-score for 67.95 inches is (67.95 - 38.2) / 1.8 = 16.53, and the Z-score for 73.95 inches is (73.95 - 38.2) / 1.8 = 19.92. Using a Z-score table or calculator, we can find the area between these Z-scores, which represents the percentage of heights in that range.
c. To find the percentage of heights that are more than 65.95 inches, we need to calculate the Z-score for 65.95 inches. The Z-score is (65.95 - 38.2) / 1.8 = 15.53. Using a Z-score table or calculator, we can find the area to the right of this Z-score, which represents the percentage of heights that are more than 65.95 inches.
d. To find the number of players in the sample who are between 61.95 and 71.95 inches tall, we need to calculate the Z-scores for both heights and find the area between those Z-scores. The Z-score for 61.95 inches is (61.95 - 38.2) / 1.8 = 13.25, and the Z-score for 71.95 inches is (71.95 - 38.2) / 1.8 = 18.86. Using a Z-score table or calculator, we can find the area between these Z-scores, which represents the percentage of heights in that range. Finally, we can multiply this percentage by the total number of players in the sample to find the number of players in that height range.
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