Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.X142 3p(x) 0.2 0.1 0.4 0.3(a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X.2X11.5P(x) 0.040.040.12(b) Refer to part (a) and calculate P(X ≤ 2.5).2.533.54× 0.04×0.16× .15× 0.09the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of(c) Again consider a random sample of size n = 2, but now focus on the statistic R =R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]RP(R)23(d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which x ≤ 1.5.]

Answer a).X Bar11.522.533.54P(X Bar)0.040.040.170.200.140.240.09b). 0.45…

Answered: Let X be the number of packages being…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 2 3 4 5 Probability 0.259 0.293 0.244 0.150 0.037 0.017 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is , so the average batch of 1000 machine parts has The standard deviation is so the typical number of defects in a batch of 1000 (Round to one decimal place as needed.)
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Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 4 Probability 0.262 0.299 0.233 0.153 0.037 0.016 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is 1.5. (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.)
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Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the x distribution is about $46 and the estimated standard deviation is about $9. (a) MULTIPLE CHOICE Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? A-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $0.23. B-The sampling distribution of x is not normal. C-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $1.42. D-The sampling distribution of x is approximately normal with mean ?x = 46 and standard error ?x = $9. (MULTIPLE CHOICE)Is it…
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