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Answer:
a) 89.97% of men have arm spans between 66 and 76 inches.
b) The z-score for this person's arm span is 5.68. 0% of males have an arm span at least as long as this person
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.
Mean of 71.4 inches and a standard deviation of 3.1 inches.
This means that
a. What percentage of men have arm spans between 66 and 76 inches?
The proportion is the pvalue of Z when X = 76 subtracted by the pvalue of Z when X = 66. The percentage is the proportion multiplied by 100.
X = 76
has a pvalue of 0.9306
X = 66
has a pvalue of 0.0409
0.9306 - 0.0409 = 0.8997
0.8997*100% = 89.97%
89.97% of men have arm spans between 66 and 76 inches.
b. A particular professional basketball player has an arm span of almost 89 inches. Find the z-score for this person's arm span. What percentage of males have an arm span at least as long as this person?
The z-score for this person's arm span is 5.68.
Z = 5.68 has a pvalue of 1
1 - 1 = 0
0% of males have an arm span at least as long as this person