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Solve the following problems (Show all your work):
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1) 2.5 percent of computer parts produced by a certain supplier are defective. What is the probability that a sample of 15 parts contains?
a) More than 3 defective ones?
b) At least one defective?
c) Less than 2 defective items?
2) On average, 1 computer in 755 crashes during a severe thunderstorm. A certain company had 2000 working computers when the area was hit by a severe thunderstorm.
a) Compute the expected value and variance of the number of crashed computers.
b) Compute the probability that less than 5 computers crashed.
c) Compute the probability that exactly 10 computers crashed.
d) Compute the probability than at least 4 computers crashed.
3) Suppose that the number of inquiries arriving at a certain interactive system follows a Poisson distribution with arrival rate of 11.35 inquiries per minute. Find the probability of 15 inquiries arriving a) In a 1-minute interval
b) in a 3-minute interval
4) Lifetimes of a certain brand of tires is approximately normally distributed with mean 38,520 miles and standard deviation 2975 miles
a) In what range do the middle 95% of tire lifetimes lie?
b) What proportion of tires last over 38,000 miles?
c) What is the median life time of the tires?
d) How far do the longest-lasting 4% of these tires roll? (What percentile are you finding here?
e) Customers get a refund if a tire has unacceptable tread that puts it in the bottom 11% of all tires. At what mileage is a customer no longer entitled to a refund?
5. A random sample of 20 girls started walking at a mean age of 12.4 months with a standard deviation of 0.75 months. A sample of 18 boys had a mean of 12 and a standard deviation of 0.65. Test the hypothesis at a 1% significance level.
6. Suppose that a sample of 39 Las Cruces residents has mean income $33,350 and standard deviation $5,185. A sample of 45 El Paso residents has mean $35,235 and standard deviation $5,810. At α=.05, does the data suggest that El Paso residents earn more than Las Cruces residents?