ADM / 2303 -Summer 2015 Assignment Four - Part two Sampling Distributions

ADM2303 -Summer 2015 

Assignment Four - Part two

Sampling Distributions

Part I of the assignment :

• Must be done via MySytatlab

• Due-date: Monday, July 27, 11:59 P.M.

Part II of the assignment :

• Please don’t forget to complete your signed statement of Academic Integrity within the body of your solution

• Submit a PDF of your type-written (i.e., not handwritten) solution (recall that a submission cannot be

marked unless it is in PDF format).

• Submit your assignment via blackboard learn by due-date Monday, July 27, 11:59 P.M.

• Make sure to provide detailed calculations and steps of how you arrived at your answer whenever needed.

Question 1.

When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for

bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample

is unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard. What is the

probability that the shipment will be accepted anyway ?

Question 2.

The average January temperature in Calgary varies from year to year. These average January temperatures

themselves have an average, over many past years, of -7.9 degrees Celsius, with a standard deviation of 5.0

degrees. Assume a Normal model applies.

a) During what percentage of years does Calgary have a January average above 0 degrees ?

b) In the 20% coldest Januaries, the average January temperature reaches no higher than how many degrees ?

c) Suppose you will be in Calgary for the next four years. Describe the sampling distribution model for the

average of the next four January average temperatures. Assume climatic conditions are not changing.

d) What is the probability that the average of the next four January average temperatures will exceed -4 degrees

? If this happens, would you consider this evidence of climactic warming (at least locally in Calgary), or

just Normal variations ?

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ADM2303 -Summer 2015 Instructor: Davood Astaraky

Question 3.

STAT2303 is a large introductory statistics course at the University of Toronto, with 720 students enrolled.

On the term test, the average score was 72, with a standard deviation of 16. There are 24 tutorials, with 30

students in each. David teaches one and Jonathan teaches another. Assume that tutorial groups are formed

quite randomly.

a) We select a student at random from Jonathan’s tutorial. Find the probability that this student’s test score

is at least 80. Assume that scores are Normally distributed.

b) We select one student at random from each tutorial. Find the probability that Jonathan’s student outperformed

David’s student by at least 7 marks on the test. Assume that scores are Normally distributed. (Hint:

work with the difference between two scores)

c) What is the probability that the average for Jonathan’s tutorial is at least 80 ? Do you need to assume that

scores are Normally distributed?

d) What is the probability that the average test score in Jonathan’s tutorial is at least seven marks higher than

the average test score for David’s tutorial? Do you need to assume that scores are Normally distributed ?

(Hint: Work with the difference between the two tutorial averages.)

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