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Lee Iacocca volunteered to drive one of his Chryslers into a brick wall to demonstrate the effectiveness of airbags used in these cars. Airbags are known to activate at random when the car decelerates anywhere from 9 to 14 miles per hour per second (mph/s). The probability distribution for the deceleration speed at which bags activate is given below.
mph/s
Probability
9
0.12
10
0.23
11
0.34
12
0.21
13
0.06
14
0.04
a. If the airbag activates at a deceleration of 12 mph/s or more, Iacocca would get hurt. What is the probability of his being hurt in this demonstration?
b. What is the mean deceleration at airbag activation moment?
c. What is the standard deviation of deceleration at airbag activation time?
Psychologists wanted to test whether a certain accelerated class' IQ was different than average. There were 25 students in the class; their mean IQ score was 108.
Your supervisor has asked you to prepare a brief report comparing the sales volumes and the consistency of sales of these four salespersons. Use the mean sales for each salesperson to compare the sales volumes.
A trigger call option forces the holder to buy a stock S at a price K if the stock price is above H at the time of expiry. Develop an analytic formula for the price of this option in a Black-Scholes world.
Suppose we have a population of scores with a mean = 200 and a standard deviation = 10. Assume that the distribution is normal. Provide answers to the following questions:
Thirty years after this research advocates still cite the first study and ignore the second study. What's the moral of this story?
A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
Calculate the test statistics
Find the probability that less than five students voted in the election and what is the probability that less than 30 accounts will be classified as delinquent?
Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time.
If active redundancy is the only means of achieving further reliability growth for each of the subsystems, what is the minimum number of redundant units of each necessary to achieve the component reliability goals?
What does it mean to compute a confidence interval "about the mean?" What does it mean to compute a confidence interval "about the proportion"?
What is the probability that a shopper will spend more than 25 minutes in a store? If 200 shoppers enter a store, how many shoppers would you expect to stay in the store for more than 25 minutes?
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