1. list the sample space S using the letters D for defective and N for non-defective computers, respectively. 2. Illustrate a probability distribution of a random variable Y showing the number of computers which are defective.
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- Make a table, compute and interpret the mean of a discrete random variable. The probabilities that a costumer will buy 1, 2, 3, 4, or 5 item in a grocery store are 3/10, 1/10, 1/10, 2/10 and 3/10 respectively. What is the average number of items that a costumer will buy?Suppose that 84% of all customers who use the service department at a certain automotive dealership would recommend the service to a friend. A random sample of 50 customers is taken. Canwe use the Normal distribution to compute probabilities about the sample proportion of thosewho would recommend the service to a friend? Why or why not?3. Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area, 25% of homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let Y be the number among the four that have earthquake insurance. (a) Find the probability distribution of Y. (b) Draw the corresponding probability histogram. (c) What is the most likely value for Y? (d) What is the probability that at least two of the four selected have earthquake insurance?
- A variable y of a finite population has the frequency distribution shown in the table. Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained. Complete parts (a) through (d) below. y 3 4 6. f 1 1 11 7 a. Determine the probability distribution of the random variable Y. 3 y P(Y = y) (Type integers or decimals. Do not round.) b. Use random-variable notation to describe the events that Y takes on the value 5, a value less than 5, and a value of at least 5. The event that Y takes on the value 5 can be represented as The event that Y takes on a value less than 5 can be represented as The event that Y takes on a value of at least 5 can be represented as { }. c. Find P(Y = 5), P(Y 5). %3D P(Y = 5) = (Type an integer or a decimal. Do not round.) P(Y<5) = (Type an integer or a decimal. Do not round.) P(Y 2 5) = (Type an integer or a decimal. Do not round.) LOThe probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at least three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at most three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) b. The probability that between two and four…Three randomly selected households are surveyed. The numbers of people in the households are 2, 6, and 7. Assume that samples of size n=2 are randomly selected with replacement from the population of 2, 6, and 7. Construct a probability distribution table that describes the sampling distribution of the proportion of odd numbers when samples of sizes n= 2 are randomly selected. Does the mean of the sample proportions equal the proportion of odd numbers in the population? Do the sample proportions target the value of the population proportion? Does the sample proportion make a good estimator of the population proportion? Listed below are the nine possible samples. 2,2 2,6 2,7 6,2 6,6 6,7 7,2 7,6 7,7 a Construct the probability distribution table. Sample Proportion Probability (Type an integer or fraction.)
- d and e only6. A study was conducted to determine the number of emergency calls per day received by the Conestoga Valley Fire Company. The data are shown here: # of phone calls Frequency 5 7 8 28 32 21 10 (a) Construct a probability distribution for the number of phone calls. (b) Find the mean number of phone calls, rounded to the nearest tenth.