3. The probability that a printer produces 0, 1, 2, 3, and 4 misprints are 15%, 22%, 10%, 38% and 15%, respectively. Construct a probability distribution table and compute the mean value, variance and standard deviation of the random variable and then interpret each value.
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- b. The peak temperature in degrees Fahrenheit, on a July day in Antaratica is a normal random variable with a variance of 225. With probability of 0.5 the temperature exceeds 10 degrees i. what is the probability that the temperature is greater than 32 degrees; ii. what is the probability that the temperature is less than 0 degree?The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. -2.1-14-0.7 0 0.7 1.4 2.1 199 200 21.3 22 22.7 234 24.1 inches inches ^^ inches 39.9 40.6 41.3 42 42.7 434 44.1 @0 10 14 18 22 26 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places) (a) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? 30 34 inchesAn online retailer operates two independent warehouses (A & B) where it keeps its inventory. Each warehouse has a .05 probability of experiencing a fire. If a fire is experienced in a given warehouse, $1,000 in inventory will be lost. What is the pooled standard deviation of the warehouses per warehouse (round to the nearest whole number)?
- 2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2Compute the variances of the two random variables whose probability tables are given in Table 7. Relate the sizes of the variances to the spread of the values of the random variables. Table 7 Outcome Probability 2 .1 4 .4 (a) 6. .4 .1 2 .3 4 .2 (b) .2 8 .3A company is producing christmas light strings containing 15 small bulbs.Suppose the success or failure of a bulb is independent of the success or failure of otherbulbs and the probability that a bulb is lightning properly is 0.85.a. When you order a christmas light string, what is the probability of at most 2 of thosesmall bulbs are not lightning properly.b. Find the mean and the variance of bulbs in a string that are not lightning properly.
- The average salary for a civil engineering major is $75,000 with a standard deviation of $10,000. A university wants to determine how well their students in their civil engineering program get paid after graduating. They ask one class of 80 students in a course to give their salaries after graduating. What is the probability the average salary of the 80 students is between $73,000 and $77,000? 0.16 O 0.93 O 0.68 O 0.78Provide each answer with three decimal places of precision. What is the weighted probability of zero days of filming? What is the weighted probability of one day of filming? What is the weighted probability of two days of filming? What is the weighted probability of three days of filming? What is the weighted probability of four days of filming? What is the weighted probability of five days of filming? What is the variance?For each situation given below, do the following: A) Decide if the random variable is Poisson (or reasonably close to Poisson). Explain your reasoning. B) If it is Poisson, find the mean and variance. C) If it is Poisson, find the probabilities indicated in the problem. 1. During the lunch rush, cars arrive at the McDonald's drive-thru line at a rate of 58 cars per hour. The arrivals are random. a. The probability of 0 cars arriving in the next half hour. b. The probability of more than 60 cars arriving in the next half hour. 2. You work for a home security sales team going door-to-door. You average 4.3 sales per day. a. The probability of no sales in a given day. b. The probability of more than 25 sales during a workweek (5 days). c. The probability of at least 250 sales over a 12 workweek summer. 3. Br. Cox plants a fixed number of bean seeds in each of his garden boxes. He is interested in the number that germinate in a given box. On average, 23 seeds germinate in each box. a. The…
- The agency for healthcare research and quality reported that 53% of people who had coronary bypass surgery in a recent year were over the age of 65. Fifteen coronary bypass patients are sampled. Let r= the number of coronary bypass patients over the age of 65. a. What is the mean of this binomial probability distribution? b. What is the variance? c. What is the standard deviation? d. Using the chebyshev's theorem for a minimum percentage of 75%, would it be unusual for 13 coronary bypass patients to be over the age of 65?2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches inches 39.9 40.6 41.3 42 42.7 43.4 44.1 19.9 20.6 21.3 22 22.7 23.4 24.1 inches - 2.1 -1.4 -0.7 0 0.7 1.4 2.1 inches 10 14 18 22 26 30 34 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)
