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 μ = 61.0 kg and standard deviation σ = 8.4 kg. Suppose a doe that weighs less than 52 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 2400 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 = 50 does should be more than 58 kg. If the average weight is less than 58 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight xfor a random sample of 50 does is less than 58 kg (assuming a healthy population)? (Round your answer to four decimal places.) (d) Compute the probability that x< 62.9 kg for 50 does (assume a healthy population). (Round your answer to four decimal places.)
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!
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 μ = 61.0 kg and standard deviation σ = 8.4 kg. Suppose a doe that weighs less than 52 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 2400 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 = 50 does should be more than 58 kg. If the average weight is less than 58 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 50 does is less than 58 kg (assuming a healthy population)? (Round your answer to four decimal places.)
(d) Compute the probability that
x
< 62.9 kg for 50 does (assume a healthy population). (Round your answer to four decimal places.)
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