Problem 1:
Consider that the age (x) of urban youth in Toronto is distributed normally, with µ = 24.7 and σ = 4.5.
a. Calculate the z-score for an age of 21.5.
b. Calculate the z-score for an x of 21.5 from a sample of size 25.
c. Explain how 21.5 can have such different z-scores.
Find the mean and standard deviation of the number of cars that have more than 1 passenger among the 500 cars stopped at a cordon-point for a survey. Assume that 5% of all cars have multiple passengers (compared to driver-only cars).
Problem 2:
The mean age for men to purchase their first home is 38 years. If the standard deviation is assumed to be 3.2 years, find the probability that a random sample of 40 men would show a mean age less than or equal to 37 years.
Problem 3:
A researcher wants to study the physical activity levels among adults. The mean weight of adult Torontonians is 135 lbs with a standard deviation of 10 lbs. She does a survey of 10 individuals who have a mean weight of 140 lbs.
a. What is the probability that the average will be 140 lbs or longer if the individuals are randomly selected?
b. If the researcher wants 10 individuals to average no more than 140 lbs less than 5% of the time, what must the population mean be, given that the standard deviation remains at 10 seconds?