Review for Exam 1
Problem 1
An inept statistics professor has a home repair
project.
• With probability 10%, he can buy the necessary
equipment at a hardware store and install it properly.
This would cost $5.
• With probability 60%, he won't be able to fix it
himself and will have to call a licensed professional.
This would cost $205.
• With probability 30%, attempting to fix it himself will
only cause additional damage. This would cost $605.
Let X be the amount of money that the project
costs. Find E(X) and SD(X).
Problem 2
In 48 patients, the amount of a certain drug in the
skin (in ng/cm2) is shown in the table below.
3
4
4
7
7
8
9
9
13
14
17
18
21
21
21
21
21
21
22
22
22
22
22
23
24
25
26
26
26
26
27
28
29
29
30
31
33
37
38
40
40
41
41
42
45
55
56
64
Draw a box-and-whisker plot for this data.
Problem 3
Draw a histogram for the data in Problem 2.
Use the right endpoint convention and the classes
0-20 ng/cm2
20-30 ng/cm2
30-70 ng/cm2
Problem 4
Five cards are dealt from a well-shuffled deck.
Find the probability that:
a)
b)
c)
d)
at least one of them is a heart
exactly two of them are hearts
the third card is a heart
the third card is heart, given that the first two
are spades
e) all five cards are hearts
Problem 5
A large data set has mean 62 and standard
deviation 14. Fill in the blanks with numbers:
a) About 68% of the data lies between _______
and _______
b) About 95% of the data lies between _______
and _______
Problem 6
A box of tickets contains 200 red tickets and 300
green tickets. Ten are selected at random. Find
(accurate to four decimal places) the probability
that exactly 6 of the tickets are red if …
a) the draws are made with replacement
b) the draws are made without replacement
Problem 7
In a certain assembly plant has three machines that
makes its products.
• Machine 1 makes 30% of the products. From past
experience, it is known that 2% of these products are
defective.
• Machine 2 makes 45% of the products. From past
experience, 3% of these products are defective.
• Machine 3 makes 25% of the products. From past
experience, 1% of these products are defective.
Suppose a randomly chosen product is found to be
defective. What is the probability that it was made by
the third machine?