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For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. Let C be the number of child tickets purchased by a single customer. The probability distribution of the number of child tickets purchased by a single customer is given in the table below: Show how to calculate the mean and standard deviation of c and determine their value.

Assume that the number of adult and child tickets purchased by a single Compute the mean and numbers of child tickets of adult tickets purchased by a single customer are 2 and 1.2 respectively. the standard deviation of the total and adult tickets purchased are independent random variables. Suppose the mean and the standard deviation for the number customer. Show your calculations. Suppose each child ticket costs $15 and of the total amount spent per purchase. Show your each adult tickets costs $25. Compute the mean and the standard deviation calculations. If the temperature in Florida falls below 32 F during certain periods of the year, there is a chance that the citrus crop will be damaged. Suppose that the probability is 0.1 that any given tree will show measurable damage when the temperature falls to 30° F. If the temperature does drop to 30 F, what is the expected number of trees showing damage in orchards of 2000 trees? Show your calculation. b. what is the standard deviation of the number of trees that show damage? Show your calculation.

inspection station fail the trs percent of all automobiles undergoing an emission inspection at a certain inspection. a. Among 15 randomly selected cars, what is the probability that at most 5 fail the inspection? Among 15 randomly selected cars, what is the probability that between 5 and 10 (inclusive) fail to pass inspection? Among 25 randomly selected cars, what is the mean value of the number that pass inspection, and what is the standard deviation of the number that pass inspection? d. What is the probability that among 25 randomly selected cars, the number that pass is within 1 standard deviation of the mean value?

The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random variable with mean u = 10 ounces and standard deviation o =1 ounce. Suppose we pick 4 tomatoes from the bin at random and put them in a bag. Let X = the weight of the bag. Show how the mean of the random variable X is calculated and find its value. ii. Show how the standard deviation (in ounces) of X calculated and find its value. The weight of a tomato in pounds (1 pound = 16 ounces) is a random variable, say Y. Determine the mean and standard deviation of Y. c. Suppose we pick 2 tomatoes at random from the bin. The difference in weights of the two tomatoes selected is a random variable, W. Find the mean and standard deviation (in ounces) of W.

An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets. a. What is the probability that Sam's first upgrade will occur exactly after the third flight? O.9.0,9 0.9 0.1= 0,0 729 b. How many flights can Sam expect to take before receiving his first upgrade? c. What is the probability that Sam will be upgraded exactly two times in his next 20 flights? Show how this probability is calculated.

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