Task 1: Uniform gaming

(4 marks total)

1. In a board game, a timer is designed to run out somewhere between 60 s and 180 s. All times are equally distributed from 60 s to 180 s.
2. What is the probability that the timer runs out in less than 100 s?(2 marks)
3. What is the probability that the timer lasts more than 130 s?(2 marks)

Task 2: What's the distribution?

(7 marks total)

1. The table below shows the heights, rounded to the nearest centimetre, of all of the students in Grade 12 at West End High School.
2. Construct a frequency polygon of these data and classify the distribution asuniform,unimodal, orbimodal.(5 marks)
3. Comment on the skewness of this distribution and explain your choice.(2 marks)
4. Height (cm)Frequency120-1291130-1392140-1496150-15914160-16920170-17923180-18911190-1996

Task 3: Middle-class incomes

(10 marks total)

1. Family incomes have a mean of $60 000 with a standard deviation of $20 000. The data are normally distributed.
2. What is the probability of a randomly chosen family having an income greater than $50 000?(3 marks)
3. What is the probability that a family income is less than $36 000?(3 marks)
4. A new tax law designed for the middle class is to help families with incomes from $45 000 to $80 000. What percentage of families will this new law help?(4 marks)

Task 4: Coffee shop scheduling

(9 marks total)

1. The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15.
2. Determine the probability that the number of customers tomorrow will be 50.(3 marks)
3. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow?(3 marks)
4. If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow?(3 marks)

Task 5: Normal approximation for binomial births

(9 marks total)

1. In Chelmsford County, the probability that a randomly chosen birth results in a boy is 45% at the local hospital. Over the course of a month, there are 20 births.
2. Is a normal approximation to the binomial random distribution appropriate here? Show your calculations and explain your choice.(3 marks)
3. Use the normal approximation to find the following probability. What is the chance that more than 14 of the births are boys?(3 marks)
4. Use the binomial probability formula to calculate the probability that more than 14 boys are born in these 20 births.(3 marks)