In this chapter, you learned about normal distributions (standard and non-standard) and binomial distributions.
Q1) For each of the following problems, identify
- the problem type,
- what data has been given, and
- for what you are asked to solve.
As an example, for one problem you might respond:
- This is a non-standard normal distribution.
- We have been given x=325, the mean = 280, and the standard deviation = 45.
- We are asked to solve for 1-p.
Remember, p is always the area to the left of x (<= X) while 1-p is the area to the right of x (>X). Also, remember that I am just trying to see if you can identify the problems. There is no need to try to solve them.
- a) The amount of a soft drink that goes into a typical 12 ounce can varies from can to can. It is distributed with a mean of 12.1 ounces and standard deviation of 0.05 ounces. What is the probability that a given can will actually contain less than the advertised level of 12 ounces?
- b) Past experience indicates that 10% of all customers going to my online store decide to buy an item. What is the probability that 10 or more of the next 30 customers who visit the website will decide to make a purchase?
- c) For a certain midterm exam, the maximum score is 120. Suppose the scores are distributed with a mean of 94 and standard deviation of 8. The instructor of this class wants to assign a grade of A to the top 15% of the students. What is the lowest you can score on the exam to earn a grade of A?
- d) Suppose the length of a typical televised regular season NHL game, from the start of play until a winner has been decided, is known to have a certain mean and standard deviation. What is the probability that a particular game will last at least a full standard deviation longer than the average?
Q2) Find the z-value or x for the values given in sheet Q2.
Q3) Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8. Solve the following questions in sheet Q3.
- a) What is the probability that a randomly selected customer spends less than $35 at this store?
- b) What is the probability that a randomly selected customer spends between $15 and $35 at this store?
- c) What is the probability that a randomly selected customer spends more than $10 at this store?
- d) Find the dollar amount such that 75% of all customers spend no more than this amount.
- e) Find the dollar amount such that 80% of all customers spend at least this amount.
Q4) This is a binomial distribution problem. In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Answer the following questions in worksheet Q4.
- a) What is the probability that exactly 5 customers will buy life insurance in the coming month?
- b) What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
- c) What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
- d) What is the probability that less than 32 customers will not buy life insurance from this agent in the coming month?
- e) Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent this month.
Now I want to know if you can correctly interpret the results of calculations. Read the problems below and then see the calculations in the worksheets. Write a one or two sentence answer stating what information is given in each calculation.
Q5) A family is moving from Bakersfield to San Francisco. Housing prices differ greatly between the two cities. The average house in Bakersfield is $240,000 with a standard deviation of $75,000 while the average house in San Francisco is $620,000 with a standard deviation of $110,000. Because of this difference in average prices, the family is concerned that their standard of living is going to change. Their house in Bakersfield just sold for $420,000.
Check out the calculation in each yellow cell of sheet Q5 (to examine the formula, just click on the cell and hit the F2 key). What do you learn from this calculation? Note that I have solved part a) for you as an example of what I am looking for.
Q6) A local company receives shipments of electronic parts from another supplier. Unfortunately, these are delicate parts to manufacture and fully 2% of all parts received turn out to be defective. Each box received from the supplier has 144 parts. A typical shipment from the supplier has 6 boxes.
Again, check out the calculation in each of the yellow cells in sheet Q6. What do you learn from this calculation? As in Q5, I have solved part a) for you.