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1) A) The lifetime of a certain type of light bulb has an exponential distribution with an average value of 200 hours

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1) A) The lifetime of a certain type of light bulb has an exponential distribution with an average value of 200 hours.(a). Calculate the first median value of the lifetime of this type of bulb and interpret this value(b). What is the 90th percentile of a bulb of the above type?  B) A certain brand of car has an average gas mileage of 35 miles per hour and a standard deviation of 5 miles per hour. If you select a car of the above brand, what is the third quartile of the gas mileage? What does this third quartile represent?

2) Suppose an electronic company sells three types of top of the line high-tech TVs at prices $4,000, $2,000, and $1,500 each, respectively. The company’s data shows that the percentages of sales of these items are 10, 60, and 30, respectively. We want to find the distribution of the sample mean and also the average revenue of selling a unit of TV across the nation.

3) Suppose an engineering firm has five engineers who are paid annual sala-ries as $70,000, $80,000, $85,000, $85,000, and $90,000, respectively.    (a). Calculate the average annual salary based on the above data.   (b). What is the median salary above?    (c). Suppose the chief executive officer (CEO), who is also an engineer, earns $180,000. How does the inclusion of the CEO’s salary in to the above data change both calculations in parts (a) and (b)?

4) John and Sam sat for two different examinations. Suppose John’s grade was 75 and the average and the standard deviation of his examination were 60 and 10, respectively. Similarly, assume that Sam’s grade was 85 and the average and the standard deviation of his examination were 90 and 0.5, respectively.     (a). Whose grade is better?    (b). Calculate z-scores for both John’s and Sam’s grades?  ( c). Interpret both z-scores.    (d). What do you think about their grades now?

5) Let X be the time (in minutes) a doctor spends to talk to a patient. Assume that this time is exponentially distributed with an average of 5 minutes.    (a)Construct the cumulative distribution function (cdf) of X.  (b)Using the above cdf, calculate the following probabilities.       a. What is the probability that the doctor spends less than 4 minutes with a patient?    b. What is the probability that the doctor spends less between 3 and 7 minutes with a patient?   c. What is the probability that the doctor spends more than 8 minutes with a patient?

6) A bicycle tire manufacturer states that the average lifetime of his tire is 3 years. If a customer purchases two bicycle tires, then calculate the probabilities.   (a)Both will survive more than 4 years?   (b)At least one will survive more than 4 years?  (c)None of them will survive more than 4 years?  (d)At least one of them will survive more than 4 years?

Assume that the height (n inches) of a certain plant can be approximated with a gamma distribution with shape parameter 2 and the scale parameter 1. If a plant of this type is selected randomly, what is the probability the height of the plant is    (a) More than 3 inches?      (b)Not more than 4 inches?