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The weight of a male bald eagle has approximately a normal distribution with mean = 7.4 pounds and a standard deviation of o=1.4 pounds. Suppose we take a random sample of n=81 male bald eagles. Let X be the random variable representing the mean weight in pounds of the 81 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 81 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 81 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 81 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the probability that 7.38 < X<7.42 pounds? h) What is the probability that Xtot >600 pounds?

The weight of a male bald eagle has approximately a normal distribution with mean = 7.4 pounds and a standard deviation of o=1.4 pounds. Suppose we take a random sample of n=81 male bald eagles. Let X be the random variable representing the mean weight in pounds of the 81 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 81 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 81 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 81 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the probability that 7.38 < X<7.42 pounds? h) What is the probability that Xtot >600 pounds?

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.CR: Chapter 13 Review
Problem 34CR
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The weight of a male bald eagle has approximately a normal distribution with mean μ= 7.4 pounds and a standard deviation of o=1.4 pounds. Suppose we take a random sample of n=81 male bald eagles. Let X be the random variable representing the mean weight in pounds of the 81 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 81 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 81 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 81 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the probability that 7.38 < X<7.42 pounds? h) What is the probability that Xtot >600 pounds?
Transcribed Image Text:The weight of a male bald eagle has approximately a normal distribution with mean μ= 7.4 pounds and a standard deviation of o=1.4 pounds. Suppose we take a random sample of n=81 male bald eagles. Let X be the random variable representing the mean weight in pounds of the 81 sampled male bald eagles. Let Xtot be the random variable representing sum of the weights of the 81 sampled bald eagles. a) About what proportion of male bald eagles have weights between 7.0 and 7.8 pounds? b) About what proportion of male bald eagles have weights greater than 7.8 pounds? c) About how many of the 81 sampled male bald eagles would you expect to have weight greater than 7.8 pounds? (nearest integer)? d) About how many of the 81 sampled male bald eagles would you expect to have weight between 7.0 and 7.8 pounds? (nearest integer)? e) What is the standard deviation of the distribution of X (in pounds)? f) What is the standard deviation of the distribution of Xtot (in pounds)? g) What is the probability that 7.38 < X<7.42 pounds? h) What is the probability that Xtot >600 pounds?
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