Use the data to develop a probability distribution for X. Specify the values for the random variable and the corresponding values for the probability function fax. B. Draw a graph of the probability distribution. C. Show that the probability distribution satisfies the required conditions for a discrete probability function. 2. The following table is a partial probability distribution for the MR. Company's projected profits x=profit in $sass for the first year of operations (the negative value denotes a loss. -100 10. 15 0 10. 20 1 50 | 0. 25 100 | 0. 30 150 10. 05 200 | I a.
What is the proper value for f(200)? B. What is the probability that MR. will be profitable? C. What is the probability that MR. will make at least $100,000? 3. A shipment of 10 items has two defective and eight nondestructive items. In the inspection of the shipment, a sample of items will be selected and tested. If at least one detected item is found, the shipment of 10 items will be rejected. A. If a sample of 3 items is selected, what is the probability that the shipment will be rejected? B. If a sample of 4 items is selected, what is the probability that the shipment will be rejected? If a sample of 5 items is selected, what is the probability that the shipment will be rejected? 4. The unemployment rate is 4. 1% (Baron's, September 4, 2000). Assume that 100 people are selected randomly. A. What is the probability that at most 5 out of 100 are unemployed? B. What is the expected number of people who are unemployed? C. What is the variance of the number of people who are unemployed? Screening facility at a major international airport. The mean arrival rate is ten passengers per minute. A. Compute the probability of no arrivals in a one - minute period. B.
Compute the probability that 3 or fewer passengers arrive in a one - minute period. 6. The lifetime (hours) of an electronic device is a random variable with the following exponential probability density function: fax=l see- ex. for a. What is the mean lifetime of the device? B. What if the probability that the device will fail in the first 25 hours of the operation? C. What is the probability that the device will operate 100 or more hours before failure? 7. The random variable X is known to be uniformly distributed between 10 and 20. A. Show the probability density function. B. Compute P(X < 15). C. Impute 8. According the the Bureau of Labor Statistics, the average weekly pay for a U. S. Production worker was $441. 84 (The World Almanac, 2000). Assume that available data indicate that production worker wages were normally distributed with a standard deviation of $90. A. Show the probability density function. B. What is the probability that a worker earned between $400 and $500 per week? C. How much did a production worker have to earn per week to be in the top 20% of the wage earners? D. For a randomly selected production worker, what is the probability that the worker earned less than $250 per week?