Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 54.0 kg and standard deviation ? = 7.8 kg. Suppose a doe that weighs less than 45 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) __ does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 54.0 kg and standard deviation ? = 7.8 kg. Suppose a doe that weighs less than 45 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) __ does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Concept explainers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 54.0 kg and standard deviation ? = 7.8 kg. Suppose a doe that weighs less than 45 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)
(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
__ does
(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)
(d) Compute the probability that x < 55.2 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)
Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x = 55.2 kg. Do you think the doe population is undernourished or not? Explain.
(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
__ does
(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.)
(d) Compute the probability that x < 55.2 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)
Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x = 55.2 kg. Do you think the doe population is undernourished or not? Explain.
Since the sample average is above the mean, it is quite likely that the doe population is undernourished.
Since the sample average is below the mean, it is quite likely that the doe population is undernourished.
Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.
Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman