BUS 273 - Problem Sheet #9
Q1. At the beginning of winter, a homeowner estimates that the probability is 0.4 that his
total heating bill for the three winter months will be less than $380. He also estimates that
the probability is 0.6 that the total bill will be less than $460.
a. What is the probability that the total bill will be between $380 and $460?
b. Given no further information, what can be said about the probability that the total
bill will be less than $400?
Q2. An investment portfolio contains stocks of a large number of corporations. Over the last
year the rates of return on these corporate stocks followed a normal distribution with mean
12.2% and standard deviation 7.2%.
a. For what proportion of these corporations was the rate of return higher than 20%?
b. For what proportion of these corporations was the rate of return between 5% and
15%?
Q3. It is estimated that the time that a well-known rock band, the Living Ingrates, spends on
stage at its concerts follows a normal distribution with a mean of 200 minutes and a
standard deviation of 20 minutes.
a. What proportion of concerts played by this band lasts between 180 and 200
minutes?
b. An audience member smuggles a tape recorder into a Living Ingrates concert. The
reel-to-reel tapes have a capacity of 245 minutes. What is the probability that this
capacity will be insufficient to record the entire concert?
c. If the standard deviation of concert time was only 15 minutes, state, without doing
the calculations, whether the probability that a concert would last more than 245
minutes would be larger than, smaller than, or the same as that found in part (b).
Sketch a graph to illustrate your answer.
d. The probability is 0.1 that a Living Ingrates concert will last less than how many
minutes? (Assume, as originally, that the population standard deviation is 20
minutes.)
Q4. According to Business Week, Maternity Chic, a purveyor of designer maternity wear,
sells dresses and pants priced around $150 each for an average total sale of $1,200. The
total sale has a normal distribution with a standard deviation of $350.
a. Calculate the probability that a randomly selected customer will have a total sale of
more than $1,500.
b. Compute the probability that the total sale will be within 2 standard deviations of the
mean total sales.
c. Determine the median total sale.
