According to the manufacturer's data, 6.5% of the items coming off the production line have a defect. Arandom sample of size 186 was obtained. Let p be the proportion of the sample that have a defect.o) to describe the probability distributionand op: (Round the answers to 4 decimal places)OF (H₂2. Find the probability that more than 9% of the sample have a defect.(Round the answer to 4 decimal places)1. Use the Central Limit Theorem (np>10 and n(1-p)>10of and state its parametersP~NN0.02op= The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widgetweights have a mean of 42 ounces and a standard deviation of 5 ounces.Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.a) 95% of the widget weights lie between 32✓and 52b) What percentage of the widget weights lie between 27 and 52 ounces?c) What percentage of the widget weights lie above 37 ?%%OB

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Answered: According to the manufacturer's data,…

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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Let X denote the mean of a random sample size n from distribution that has mean U and variance o = 10. Find the sample size n, so that the probability is approximately =0.954 %3D that the random interval X -5,X+5 | contains U is Select one: a. n=100 b. n= 40 C. n = 80 d. n = 160
Suppose that X follows a binomial distribution with n = 100 and p = 0.1. If F(x) is the cumulative distribution function of the Standard Normal distribution. Then using the Normal approximation, the probability P(X = 16) is obtained by O a. F(2.17) - F(1.83) O b. F(1.83) - F(2.17) O c. F(16.5) + F(15.5) O d. F(17.0) - F(15.0)
8. Be X a discrete random variable with distribution given by: Select one: a. 1/8 b. 1/4 c. 3/8 d. 5/8
Assume that the random variable X is normally distributed, with mean r=80 and standard deviation a=12. Compute the probability P(X < 95).
Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following. a. P(X > 5000) = b. For an exponential random variable with the same mean as the Weibull distribution P(X > 5000) =
Suppose (S, P) is a binomial distribution with n trials and probability of success p. Let X be the random variable X(k) = k³, where k is the number of successes. Calculate E[X].
Q3. A random variable X is normally distributed with µ= 50 and o² = 25 . Find the %3D Probability (a) that it will fall between (i) 0 and 40 (ii) 55 and 100 (b) that it will be (i) large than 54 (ii) smaller than 57
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.
Let X1, . . . , X7 independent random variables with exponential distribution of parameter λ = 2. What distribution has the next sum?
On a popular app, users rate restaurants as 1, 2, stars of the selected rating. Here is the probability distribution of XX. Value x of X 2 ly selected from all the ratings on the app. Let X be the number of WER P(X=x) 0.21 0.20 0.11 0.24 0.24 For parts (a) and (b) below, find the probability that the randomly selected restaurant rating has the described number of stars. (a) 3 or more: (b) Fewer than 4:
The profits of a mobile company are normally distributed with Mean of R.O (17x 10) and standarddeviation of R.O (17).a. Find the probability that a randomly selected mobile has a profit greater than R.O ((17x10) +10)
A sample of n = 20 observations is drawn from a normal population with u = 1100 and o = 180. Find each of the following: A. P(X > 1176) Probability = B. P(X 1063) Probability =

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