a. Let Z ~ Normal(0, 1) be a continuous standard normal random variable with mean of0 and standard deviation of 1. What is the probability that Z comes out to be lessthan -1.64?Normal(26.2, 5) is a continuous normal random variable26.2 and standard deviation of o = 5. What is the probability thatb. Suppose instead that X ~with mean of µ =X comes out to be less than 18?c. Working still with XThat is, find a value c such that the probability that X is bigger than c is 2.5%.Normal(26.2, 5), find a value c such that P(X > c) = 0.025.

Part a) It is given that the random variable is a standard normal variable with mean 0 and standard…

Answered: a. Let Z ~ Normal(0, 1) be a continuous…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 ? = 53.0 kg and standard deviation ? = 8.7 kg. Suppose a doe that weighs less than 44 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 2150 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 = 80 does should be more than 50 kg. If the average weight is less than 50 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 80 does is less…
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Please note the question is: What is the distribution of the t-test statistic if m, n -----> ∞ ?
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the standard normal distribution is just a normal distribution with μ = 0 and σ^2 = 1. it turns out that if we standardize a normal random variable X with parameters μ, σ in the following way z = x-μ/σ the expected value of the transformation is 0 and variance is 1. so if Z = 0.2, when μ=3 and σ= 0.2, what is the normal random variable X has value?
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