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 app normal with mean u = 57.0 kg and standard deviation o = 7.9 kg. Suppose a doe that weighs less than 48 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.) 0.1271 (b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) 299 v does (c) Tc estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 54 kg. If the average less than 54 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 55 d than 54 kg (assuming a healthy population)? (Round your answer to four decimal places.) 0.0024 (d) Compute the probability that x < 58.6 kg for 55 does (assume a healthy population). (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 55 does in December, and the average weight was x = 58.6 kg. Do you think the doe population is undernouris Explain. O Since the sample average is above the mean, it is quite likely that the doe population is undernourished. O Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. O Since the sample average is below the mean, it is quite likely that the doe population is undernourished. O Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.
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 app normal with mean u = 57.0 kg and standard deviation o = 7.9 kg. Suppose a doe that weighs less than 48 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.) 0.1271 (b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) 299 v does (c) Tc estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 54 kg. If the average less than 54 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 55 d than 54 kg (assuming a healthy population)? (Round your answer to four decimal places.) 0.0024 (d) Compute the probability that x < 58.6 kg for 55 does (assume a healthy population). (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 55 does in December, and the average weight was x = 58.6 kg. Do you think the doe population is undernouris Explain. O Since the sample average is above the mean, it is quite likely that the doe population is undernourished. O Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. O Since the sample average is below the mean, it is quite likely that the doe population is undernourished. O Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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
Transcribed Image Text: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 ap-
normal with mean u = 57.0 kg and standard deviation o = 7.9 kg. Suppose a doe that weighs less than 48 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.)
0.1271
(b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
299
does
(c) Tc estimate the health of the December doe population, park rangers use the rule that the average weight of n = 55 does should be more than 54 kg. If the average
less than 54 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 55 d-
than 54 kg (assuming a healthy population)? (Round your answer to four decimal places.)
0.0024
(d) Compute the probability that x < 58.6 kg for 55 does (assume a healthy population). (Round your answer to four decimal places.)
Suppose park rangers captured, weighed, and released 55 does in December, and the average weight was x = 58.6 kg. Do you think the doe population is undernouris
Explain.
O Since the sample average is above the mean, it is quite likely that the doe population is undernourished.
O Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.
O Since the sample average is below the mean, it is quite likely that the doe population is undernourished.
O Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.
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