STAT
251G
Online
class
Name_________________________________
Date___________________
1. A couple plans to have 3 children. How many possible outcomes are there? Draw a tree diagram to show the sample
space. What is the probability that they
will have exactly 2 girls and 1 boy?
2. The
number of cartoons watched on Saturday mornings by students in Mrs. Kelly’s
first grade class is shown below.
Number of cartoons watched X
0
1
2
3
4
5
Probability P(X)
0.15
0.20
0.30
0.10
0.20
0.05
Find the
mean, variance, and standard deviation.
Show the correct formulas and your work.
3 Find the zvalue
to the right of the mean such that 85% of the total area under the standard
normal distribution curve lies to the left of it? Explain how you found your answer.
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4. The mean weight of loads of
rock is 43.0 tons with a standard deviation of 10.0 tons. If 25 loads are chosen at random for a weight
check, find the probability that the mean weight of those loads is less than
41.9 tons. Assume that the variable is
normally distributed. Show all work,
including your sketch of the normal distribution with the correct area shaded.
5. Mrs. Smith’s reading class
can read an average of 175 words per minute with a standard deviation of 20
words per minute. The top 3% of the
class is to receive a special award. What is the minimum number of words per
minute a student would need to read in order to get the award? Assume the data is normally distributed. Show all work.
6. Many statistical methods require that
the distribution of data is approximately normal. Minitab has several
tests that can help determine normality, and Excel uses a normal quantile plot
to determine normality.
Use Minitab or
Excel to determine if the following distribution is normal. Follow the
instructions in the Technology section of 6.2
Enter the data from Page 325
Problem #40 or you can use the data file:
Cut and paste your results
into a word document.
7. Game: Roll two dice and record the sum. You must pay $1.00 to play
the game. The payout is as follows:
A sum of
2 or 12 $3.00
A sum of
3 or 11 $2.00
A sum of
4 or 10 $1.00
Any
other sum $0.00
Play the game 25 times and use the table to record your
results.
Turn
Sum
Win
Pay
Return
1
3
$2.00
$1.00
$1.00
2
6
$0.00
$1.00
-$1.00
3
9
$0.00
$1.00
-$1.00
4
3
$2.00
$1.00
$1.00
5
11
$2.00
$1.00
$1.00
6
9
$0.00
$1.00
-$1.00
7
6
$0.00
$1.00
-$1.00
8
9
$0.00
$1.00
-$1.00
9
11
$2.00
$1.00
$1.00
10
3
$2.00
$1.00
$1.00
11
12
$3.00
$1.00
$2.00
12
4
$1.00
$1.00
$0.00
13
6
$0.00
$1.00
-$1.00
14
3
$2.00
$1.00
$1.00
15
8
$0.00
$1.00
-$1.00
16
6
$0.00
$1.00
-$1.00
17
9
$0.00
$1.00
-$1.00
18
7
$0.00
$1.00
-$1.00
19
8
$0.00
$1.00
-$1.00
20
3
$2.00
$1.00
$1.00
21
5
$0.00
$1.00
-$1.00
22
6
$0.00
$1.00
-$1.00
23
2
$3.00
$1.00
$2.00
24
2
$3.00
$1.00
$2.00
25
7
$0.00
$1.00
-$1.00
Total
-$1.00
Average
-$0.04
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