The University of British Columbia

here are 81 and 64 students in two sections of Stat 302. It is known that the mean mark of Section 1 is 71% and of section 2 is 73%. The variance of individual marks is 0.25 for all students. Assume grades are independent of each other. Let X = the average mark of section 1; Y = the average mark of section 2. (a) Calculate E(X − Y ) and Var(X − Y ). (b) Calculate P (X − Y ≤ 3) by normal approximation

Assume that the number of customers arriving at the restaurant has a Poisson distribution with an average of 40 per hour. (a) Give an expression for the probability that twenty, 2 minutes in- tervals have to be observed to find 5, in which exactly 4 customers arrive in the first 2 minutes. (b) Find the probability that the time between consecutive customers arriving is between 1/4 and 1/2 minute.

Measurements of the levels of exposure to carbon monoxide (CO) on 17 domestic ConAir flights yield ̄x = 63ppm and s = 5.4ppm. The air quality is acceptable if the mean amount of CO is less than 70ppm. Do the data provide sufficient evidence that the air quality on ConAir flights is acceptable? Test at α = 0.05

Scandals of a celebrity are distributed uniformly throughout the year with an average of 1 per every 90 days. (a) Calculate the probability that 5 such scandals occurred in a period of 360 days? (b) Given that 5 such scandals occurred in a period of 360 days, what is the probability that 4 of them occurred in the first 90 days? (c) Find the probability that in a period of 90 weeks (each has exactly 5 days), 85 weeks are scandal free. (d) Find a suitable approximation to the probability in (c)

An individual who has automobile insurance from a certain company is randomly selected. Let X be the number of violations for which the individual was cited during the last three years. The probability distribution of X is: x: 0 1 2 3 P (X = x): 0.6 0.2 0.15 0.05 (a) What is the probability that the individual is cited for exactly 2 violations? (b) What is the probability that the individual is cited for at least 1 violation? (c) Find the mean and standard deviation of X

The lengths (cm) of a random sample of adult male Chinook salmon from the Nanaimo River gave the following summary statistics: ̄x = 80.5 s = 10.5 Q1 = 75.5 M edian = 84 Q3 = 96 (a) Approximately what proportion of the lengths is between 75.5cm and 96.0cm? (b) At least what proportion of the lengths is between 59.5cm and 101.5cm? (c) Assuming a normal distribution, what proportion of the lengths is above 91.0cm? (d) Assuming a normal distribution, what proportion of the lengths is between 70.0cm and 112cm? (e) If the longest 84% of these fish can be retained, what is the minimum retention length?