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Applying The population of adult women in the United States has a mean height of 65 inches (5'5") and a standard deviation of 3.5 inches. Let X = the height of an American female. Thus, X~ N(65, 3.5). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of lowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) a. What is the probability of randomly selecting a female shorter than 58 inches tall? P(X < 58) = (Include five decimal places.)

Applying The population of adult women in the United States has a mean height of 65 inches (5'5") and a standard deviation of 3.5 inches. Let X = the height of an American female. Thus, X~ N(65, 3.5). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of lowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) a. What is the probability of randomly selecting a female shorter than 58 inches tall? P(X < 58) = (Include five decimal places.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 7E
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Applying the Normal Distribution and Central Limit meorem The population of adult women in the United States has a mean height of 65 inches (5'5") and a standard deviation of 3.5 inches. Let X = the height of an American female. Thus, X~ N(65, 3.5). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of lowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) a. What is the probability of randomly selecting a female shorter than 58 inches tall? P(X < 58) = (Include five decimal places.) b. Determine the 90th percentile for the distribution. (This Normal Distribution Percentile Calculator may be useful.) X = inches. (Include one decimal place.) c. If 100 women were randomly chosen, what is the probability that the sample mean of this group would be less than 64.5 inches? P(X < 64.5) = = (Include five decimal places.)
Transcribed Image Text:Applying the Normal Distribution and Central Limit meorem The population of adult women in the United States has a mean height of 65 inches (5'5") and a standard deviation of 3.5 inches. Let X = the height of an American female. Thus, X~ N(65, 3.5). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of lowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) a. What is the probability of randomly selecting a female shorter than 58 inches tall? P(X < 58) = (Include five decimal places.) b. Determine the 90th percentile for the distribution. (This Normal Distribution Percentile Calculator may be useful.) X = inches. (Include one decimal place.) c. If 100 women were randomly chosen, what is the probability that the sample mean of this group would be less than 64.5 inches? P(X < 64.5) = = (Include five decimal places.)
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