8. Suppose that you are dealt four cards, at random, from a standard deck.
a.
What is the probability that exactly three of these cards will be spades?
b.
What is the probability that at least three of these cards will be spad
10. MBS10, problem 3.17, pag
11. The apples from HappyMac Farm have diameters which are approximately normally
distributed with mean = 3.0 inches and standard deviation = 0.3 inch. Apples can be
size-sorted by being made to roll over a mesh screen.
a.
If a batch of apples is rolled o
HINT 1:
HINT 2:
HINT 3:
Based on your solution to the previous problem, you see that n = 500
is not large enough.
You will have to proceed by trial and error, e.g., try 600 and then
narrow it down until you get what you want.
You want P[ X 310 ] to be 0.9
STAT-UB.0103
Sample exam 1
. The daily gross receipts at the Happy-Go-Lucky Supermarket have a long-run average
of $140,000, with a standard deviation of $18,000. Find the probability, that on any day
(a)
the gross receipts will exceed $131,000.
(b)
the g
1. You have been tracking the cash reserve of a very large mutual fund, hoping to find clues
about future behavior. The cash reserve is currently at 4.32. The units here are millions of
dollars. You believe that the daily changes to this reserve are norma
1. The random variable Y has the probability distribution described in this table:
y
P[ Y = y ]
1
0.20
2
0.50
3
0.20
4
0.10
Find the mean and standard deviation of the random variable Y.
2. The random variable Q has the probability distribution described
2. Please indicate true or false for each of the following. The problem is worth 20
points, and there are ten parts. The score is 2 correct wrong.
_ (a) In any set of numbers, it must happen that UQ.
_ (b) It is possible for the average of a set of number
3. Pearl Emporium obtains its womens sweaters from a cut-rate workshop that has very low
prices but also very bad quality control. The sweaters are packed in cartons of 60. The
managers at Pearl have the option of doing a sampling inspection before they a
HOMEWORK SET 4
STAT-UB.0103
The file M\MONET.mtp has information on 430 Monet paintings sold at
auction. Column C27 gives the sales price in United States dollars.
(a)
Give a 95% confidence interval for the population mean. This is
automated in Minitab th
16. In games of the KENO or LOTTO style, the bettor selects numbers from a fixed set.
Then the game operator selects another set of numbers, and the bettor wins according to
the number of matches.
a.
Suppose that the game uses the numbers 1 through 50, an
4. If two dice are rolled together, what is the probability that
a.
the total number of spots is 8;
b.
the total number of spots is 4;
c.
both dice show the same number;
d.
at least one of the dice shows the number six?
e.
neither of the dice shows the nu