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Spring 2015
Math 227
FINAL
Name: ______________________
Show your work clearly, neatly, and understandably. Make sure you round the decimal for probability to 5-decimal place and round
the percentage to 3-decimal. 110 points available.
1.
a.
McDee fast food conducted a taste survey before marketing a new fruit salad. The results of the
survey showed that 70% of the people who tried this salad liked it. Encouraged by this result, McDee
decided to market the new salad. Assume that 70% of all people like this salad. On a certain day, eight
customers bought it for the first time.
What is the probability that at least 5 customers like this new fruit salad?
b.
What is the mean and standard deviation of this probability distribution?
2.
Let P A  0.4, PB  0.6 and PB | A  0.3 .
a. P A  B
(6:3,3)
(8:2 each)

d. P B | A

b. P A | B

c. P A  B
3.

(4) A company
that produces candy wants to estimate the mean amount of candy in 64-ounce box at a 99%
confidence level. The company knows that the standard deviation of amounts of candy in such box is 0.2
ounce. How large a sample should the company take so that the estimate is within 0.04 ounce of the
population mean?
By design, the scores on the SAT Math are N(500,1002)-distributed.
4.
(17:3,4,4,6)
a.
Find the probability that an SAT Math test-taker
score higher than 620.
c.
Find the probability that the average score of 9
SAT Math test-takers is higher than 620.
b.
Find the probability that at least 5 out of 9 SAT
Math test-takers score higher than 620.
d.
Find the minimum average score of 9 SAT Math
test-takers to be in the top 1%.
5.
(10:4,6) A box
a.
replacement:
What is the probability of selecting 1 red and 1
green marble?
contained 3 red, 4 green, and 2 blue marbles. Select 2 marbles randomly without
b.
What is the probability of selecting a green
marble given that the other one is non green
color?
6.
c.
claims that teenagers in America spend an average of 18 hours a week on sport. A
teacher wanted to test this claim. She took a sample of 10 students and asked them about the time they
spend on sport per week. Their responses are: 14, 25, 22, 38, 16, 26, 19, 23, 41, 33. Assume that the times
spent on sport by all teenagers are normally distributed. Find:
The median.
g. At 5%-SL, is there sufficient evidence to
The first quartile.
support the claim that teenagers in America
spend an average of 18 hours a week on sport?
The third quartile.
d.
The range.
e.
The sample mean and sample standard deviation
of these 10 students.
f.
Construct a 95%-CI for the standard deviation
of the time American teenagers spend on sport
in a week.
a.
b.
(22:1,1,1,1,5,6,7) A study
7.
The following table shows Helmet Use and Risk of Head Injuries in Alpine Skiers and
Snowboarders. Use it to answer the following questions.
(9:3,3,3)
Head Injuries
a.
Not Injured
Wore Helmet
96
656
No Helmet
480
2330
If one person is randomly selected, write the
notation and find the probability of selecting
c.
If two people are randomly selected, find the
probability that they both wore helmets.
someone who had a head injury or wore a
helmet.
b.
If one person is randomly selected, write the
notation and find the probability of selecting
someone who did not wear a helmet, given that
person was with head injuries.
8.
(5) A box
contains 3 red balls and 2 blue balls. Two balls are drawn, one at a time.
If the first ball is red, it is kept out of the box and a second ball is drawn from the box.
If the first ball is blue, then it is put back in the box, a new red ball is added to the box, then a
second ball is drawn from the box.
If the second drawn ball is red, what is the probability that the first drawn ball was blue?
9.
(6)
In a sample of 800 Americans, 352 considered themselves at least somewhat overweight. Construct a
96%-CI for population proportion of Americans who consider themselves at least somewhat overweight.
10.
(9) A researcher
wanted to investigate if the male and female workers in a state commute the same
distance to work. A sample of 500 male workers showed that they commute an average of 21 miles to
work with a standard deviation of 5.2 miles. A sample of 400 female workers gave an average commuting
distance of 16 miles with a standard deviation of 4.4 miles.At 2%-SL, can we conclude that the mean
commuting distances are different for male and female workers in this state?
11.
The following is the distribution of sales made by two branches of a grocery store on 7 randomly
selected dates.
(14:6,8)
Date
Anaheim
Irvine
25-Nov
8500
8200
2-Feb
2800
2700
5-May
4200
4000
25-Aug
5600
4900
25-Apr
5700
5300
12-Jun
7300
7000
21-Dec
10000
9200
Can we conclude that the average daily sales at Anaheim branch is at least $200 more than the average daily
sales at Irvine branch?