According to Mars, Incorporated, 20.5% of the M&M'S® Milk Chocolate Candies made at itsCleveland factory are orange. Assume that the company's claim is true. Suppose you take arandom sample of 8 candies from a large bag of M&M'S. Let X = the number of orangecandies you get.Orange M&M'Sa. Explain why it is reasonable to use the binomial distribution for probabilitycalculations involving X.b. What's the probability that you get 3 orange M&M'S?c. Calculate P(X ≥ 4). Interpret this result.d. Suppose that you get 4 orange M&M'S in your sample. Does this result provideconvincing evidence that Mars's claim about its M&M'S is false? Justify youranswer.Orange M&M'Sa. Find and interpret the expected value of X.b. Find and interpret the standard deviation of X.

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Answered: According to Mars, Incorporated, 20.5%…

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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suppose we select an SRS of 1010 adults. If it is believed that 60% of all adults are very satisfied with their lives, what is the probability that at least 610 adults in our sample are very satisfied with their lives?Let X be the number (out of 1010) of adults who are very satisfied with their lives. What distribution should X have? Why?
The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 53.9%. What is the probability that in a random sample of 430 voters, less than 49.2% say they will vote for the incumbent?
Suppose that a recent poll found that 50% of adults in a certain country believe that the overall state of moral values is poor. If a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (e) below. Click here to view the table for the binomial probability distribution. Click here to view the table for the cumulative binomial probability distribution. ..... (a) Find and interpret the probability that exactly 9 of those surveyed feel the state of morals is poor. The probability that exactly 9 of those surveyed feel the state of morals is poor is. (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. In 100 trials of this experiment, we expect about to result in exactly 9 adults who feel the state of morals is poor. (b) Find and interpret the probability that no more than 3 of those surveyed feel the state of morals…
The auto parts department of an automotive dealership sends out a mean of 4.4 special orders daily. What is the probability that, for any day, the number of special orders sent out will be no more than 5? Round your answer to four decimal places.
Suppose you are going to draw 20 cards, with replacement, from a deck of 52 cards and record the proportion of draws that are red. There are 26 red and 26 black cards in a typical deck of cards. You draw the 20 cards, replacing each card between draws, and 2/20 cards drawn are red. Are you suspicious about the fairness of this deck of cards? Simply list the answer to your probability calculation and explain your reasoning.
Based on historical data, your manager believes that 26% of the company's orders come from first-time customers. A random sample of 146 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.28 and 0.46?
Based on historical data, your manager believes that 25% of the company's orders come from first-time customers. A random sample of 79 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.31?
Your manufacturing plant produces air bags, and it is known that 50% of them are defective. Five air bags are tested. Compute the probability distribution of the binomial variable described above, and use it to compute the probability that if five air bags are tested, at least one will be defective and at least one will not.

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