Some parts of California are particularly earthquake-prone. Suppose that in one

Question

Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 31% of all home owners are insured against earthquake damage. Four home owners are to be selected at random. Let X denote the number among the four who have earthquake insurance. Find the probability distribution of X. (Round your answers to. four decimal places.) What is the most likely value for X? What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.) A consumer organization that evaluates new automobiles customarily reports the number of major defects in each car examined. Let X denote the number of major defects in a randomly selected car of a certain type. The cdf of X is as follows:

Explanation / Answer

PART A.

Note that the probability of x successes out of n trials is  
  
P(n, x) = nCx p^x (1 - p)^(n - x)  
  
where  
  
n = number of trials =    4
p = the probability of a success =    0.31
x = the number of successes

Hence, the table:

a)

c)

The highest probability is at

x = 1. [ANSWER]

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d)

P(at least 2) = P(2) + P(3) + P(4) = 0.36597763 [ANSWER]

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x 0 1 2 3 4 P(x) 0.226671 0.407351 0.274519 0.082223 0.009235

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