Question

In: Statistics and Probability

Suppose that 30% of all homeowners in an earthquake-prone area of California are insured against earthquake...

Suppose that 30% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.

(a) Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.3)(.7)(.3)(.3) and associated x value of 3. There are 15 other outcomes.)

Value of x Probability
0
1
2
3
4



(b) What is the most likely value of x?

0

1

1 and 0

3

4



(c) What is the probability that at least two of the four selected homeowners have earthquake insurance?
P (at least 2 of the 4 have earthquake insurance) = ______

Solutions

Expert Solution

a)

P(X=x)=

x P(x)
0 0.2401
1 0.4116
2 0.2646
3 0.0756
4 0.0081

b) most likely value of x = 1

c)P (at least 2 of the 4 have earthquake insurance) = 0.2646+0.0756+0.0081 =0.3483


Related Solutions

Suppose that 20% of all homeowners in an earthquake-prone area of California are insured against earthquake...
Suppose that 20% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance. (a) Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.2)(.8)(.2)(.2) and associated x value of 3. There are 15 other outcomes.)
The chance a home owners is insured against an earthquake is.35. A sample of four...
The chance a home owners is insured against an earthquake is .35. A sample of four homeowners is selected at random. Suppose X is a random variable that is modeled by a binomial distribution which describes the number of homeowners out of four that have insurance. Find the probability mass function of X when x = 0, 1, 2, 3, and 4. Then find what is the most likely value of x. Find the probability that at most 1 of...
A statistician has correctly predicted every earthquake in California for the past 30 years, as follows:...
A statistician has correctly predicted every earthquake in California for the past 30 years, as follows: Each day, the statistician predicts an earthquake. That way, whenever there's an earthquake, he can say that he correctly predicted it. What, if anything, is wrong with the statistician's logic?
Adverse Selection: Suppose Snake Farm insurance provides fire insurance coverage to 10,000 homeowners in California.
Adverse Selection: Suppose Snake Farm insurance provides fire insurance coverage to 10,000 homeowners in California. Based on historical data, Snake Farm’s expert statisticians (a.k.a actuaries) have calculated that in a given year on average 100 of Snake Farms customers will lose their homes due to a fire. The historical data also shows that the average cost of replacing a house is $100,000.Assuming that Snake Farm’s must charge the same insurance premium to all its customers, how much will Snake Farm...
The dataset HomesForSaleCA contains a random sample of 30 houses for sale in California. Suppose that...
The dataset HomesForSaleCA contains a random sample of 30 houses for sale in California. Suppose that we are interested in predicting the Size (in thousands of square feet) for such homes. State Price Size Beds Baths CA 500 3.2 5 3.5 CA 995 3.7 4 3.5 CA 609 2.2 4 3 CA 1199 2.8 3 2.5 CA 949 1.4 3 2 CA 415 1.7 3 2.5 CA 895 2.1 3 2 CA 775 1.6 3 3 CA 109 0.6 1...
According to past data, the 15% of all college students in California are business majors. Suppose...
According to past data, the 15% of all college students in California are business majors. Suppose a random sample of 200 California college students is taken. a) What information about this sample allows us to use the normal distribution for our sampling distribution? b) Calculate the standard error. Round to two places for ease. c) What is the probability that the sample of 200 gives a sample proportion of 18% or higher? Show your calculator function and entries. Round to...
Suppose that on Friday, a company announces a new vaccine with99% effectiveness against all variants,...
Suppose that on Friday, a company announces a new vaccine with 99% effectiveness against all variants, available in late 2021. What will happen to the price of 10 year Treasuries?A. The price fallsB. The price rises
1. Suppose the lengths of all fish in an area are normally distributed, with mean μ...
1. Suppose the lengths of all fish in an area are normally distributed, with mean μ = 29 cm and standard deviation σ = 4 cm. What is the probability that a fish caught in an area will be between the following lengths? (Round your answers to four decimal places.) (a) 29 and 37 cm long (b) 24 and 29 cm long 2.   The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with...
1) Suppose that all five of the producers of readymix cement in the Denver area have...
1) Suppose that all five of the producers of readymix cement in the Denver area have entered into a cartel agreement, so that they are producing and pricing at the profit-maximizing monopoly level. a. How would a firm’s managers “cheat” on this agreement? b. Given that the four other competitors’ reactions are not instantaneous, can cheating be profitable? 2) In a small town, the managers of the three janitorial service firms have tacitly agreed to charge $150 per week for...
PLEASE answer all parts :) 1. Suppose public opinion is split 60% against and 40% for...
PLEASE answer all parts :) 1. Suppose public opinion is split 60% against and 40% for increasing taxes to help balance the federal budget. 300 people from the population are selected randomly and interviewed. a) The sampling distribution of the sample proportion of people who are against increasing taxes to help balance the federal budget has a mean of _____ and a standard deviation of _______. b) What is the probability at least 65% of the people in the sample...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT