## Sun4.vaniercollege.qc.ca

(1) (2.5 marks) The weight (pounds) of n = 8 female wolves captured in the Yukon-Charley National Reserve are {57, 84, 90, 71, 77, 68, 73, 72}. As-suming that the weight distribuiton of female wolves is normally distributedconstruct a 95% confidence interval for the population mean.
(2) (3 marks) The weekly demand for the common antibiotic Amoxicillin (in 1000’s of pills) at a pharmacy is a random variable X with probability density a) Compute the mean and the variance.
b) What is the probability that in one year (52 weeks) the total number ofAmoxicillin pills dispensed at this pharmacy will be more than 85,000? (3) (2 marks) A medical policy research team has collected data for patients with a heart attack (myocardial infarction), summarized in the following jointprobability table.
Here, X is the severity of the heart attack, with 1=acute, 2=serious, 3=mildand Y is the type of hospital where the patient was treated, with 1=Level 1Trauma Center, 2=Research Hospital, 3-Commuinity Hospital.
a) What percentage of patients were treated at a Research Hospital?b) What is the probability that a patient treated at Level 1 Trauma Centerhad an acute heart attack?c) What is the probability that a patient treated at a Community Hospitalhad an acute or a serious heart attack?d) What is the probability that a patient with a mild heart attack will betreated at Community Hospital? (4) (2 marks) A survey found that the students at Vanier party on average 8 hours a month with standard deviation of 3 hours, while the students atSaint-Laurent party on average 13 hours with standard deviation of 4.5 hours.
What is the probability the average monthly party time of a group of 33Vanier students will be at least 4 hours less than the average party time of agroup of 36 Saint-Laurent students.
(5) (2 marks) The credit card processing time at Amazon.ca is exponentially dis- tributed with an average of 90 seconds.
a) Find the probability that the processing time will be more than a minute?b) What range of response times contains at least 95% of all response times? (6) (2 marks) The daily sales X (in hundreds of dollars) of Stan der Deviation, an itinerant snake oil salesman have probability density function: a) Determine the cumulative distribution.
b) What is the probability that Stan will have sales exceeding 400\$ in a day? (7) (2 marks) A manufacturer of semiconductor chips produce 3% defective chips.
Estimate the probability that at least 30 to at most 35 chips are defective ina random sample of 1000 chips.
(8) (2 marks) Many students work part time during the school year. To determine the hours a week a typical student works, a random sample of 108 workingstudents is selected. The responses to the question ”How many hours did youwork last week?” had mean of 13.4 hours and a st. dev. of 4.8 hours.
a) Construct 95% and 99% confidence intervals for the average number ofhours a week a typical student works.
b) How large a sample is needed to find the population average with maxi-mum error of half an hour and 99% confidence? (9) (2.5 marks) Abe and Bill, are sommeliers at one of the swankiest restaurants in NYC. In particular, they sample and assign quality ratings to wines. Theratings are on a three point scale: {−1, 0, 1}. Let X be the rating given byAbe and let Y be the rating given by Bill. The following table gives the jontprobability distribution of X and Y .
a) Determine the average ratings given by Abe and by Bill?b) Determine the variances of the ratings by Abe and by Bill.
c) Determine the correlation between Abe’s and Bill’s ratings.

Source: http://sun4.vaniercollege.qc.ca/~iti/2013/probstatA13/test2.pdf

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