4) Suppose Cal Crouk is a crooked politician. Suppose that, on average, he lies 2 times ina five minute stretch. Suppose Cal has a half hour speech planned, and let X be thenumber of lies in Cal's speech.a) How is X distributed?b) What is the mean and variance of Xc) What is the probability that Cal lies exactly 20 times?

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Answered: 4) Suppose Cal Crouk is a crooked…

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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11) Suppose we have a distribution of the number of "friends" all users of a popular social media site have. What measure of spread would be best to describe this data? A) spread should be described with the IQR because the distribution will be symmetric. B) The spread should be described with the IQR because the distribution will be skewed to the right. C) The spread should be described with the standard deviation because the distribution will be symmetric. D) The spread should be described with the standard deviation because the distribution will be skewed to the right.
Find the mean of the probability distribution of the number of heads obtained in 5 flips of a fair coin. 1 оооо 5/2 2/5 1/5
There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
16. For a recent period of 100 years, there were 530 Atlantic hurricanes a) State the distribution, the parameters (for each case) and the support of the distribution. b.) Find the probability that over a period of 2 years there are fewer than 5 hurricanes. c.) Find the probability that over a 5 year period there are 10 hurricanes. d.) Find the probability that at least 2 hurricanes happen in a year.
5) Samples of size n = 2 are randomly selected with replacement from the popula- tion consisting of 2, 4, and 10, where the values represent the number of people in households. 5a) Find the mean of each of the nine samples and summarize the data in the form of a probability distribution. seroMvT as borolgo olgouq Ind upo o t te bas io 5b) Compare the population mean to the mean of the sample means in this example. Does this support the idea that sample means do not target the population means?
3. A company produces boxes of candy that contain a mean of 50 candies each. The standard deviation is 2. Quality control will reject any box with fewer than 48 candies. a) What is the probability that a box selected at random contains exactly 51 pieces? b) What proportion of the boxes will quality control reject as containing too few candies? c) The company produces 135 000 boxes of candy a day. How many of these boxes will have at least 48 candies but no more than 53?
c) If the probability that a person scores below a particular value is 0.7, then the probability a person scores above that value equals? d) If the probability that a person scores between a particular positive z value and the mean is 0.31, then the probability a person scores above that value equals?
Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?

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