# tissues probability

```Chapter 2
CQ1) Which variable is least likely to be regarded as ratio data?
a. Length of time required for a randomly-chosen vehicle to cross a toll bridge (minutes).
b. Weight of a randomly-chosen student (pounds).
c. Number of fatalities in a randomly-chosen traffic disaster (persons).
d. Student's rating of a professor's performance (Likert scale).
CQ2) Your rating of the food served at a local restaurant using a 3-point scale of 0 = gross, 1 = decent, 2
= yummy is ___________ data.
a. nominal.
b. ordinal.
c. interval.
d. ratio.
CQ) The mean and median of a certain variable, were given to be \$25,000 and \$31,000 respectively.
What is the shape of the distribution?
a. Left Skewed
b. Symmetric
c. Right Skewed
d. Cannot be determined from the given information.
1) Given P(A) = 0.5; P(B) = 0.4 and P(A and B) = 0.15. Applying the General law of Addition, what is
P(A or B)?
a)
b)
c)
d)
0.15
0.2
0.7
0.75
2) Given P(A) = 0.6; P(B) = 0.4 and P(A and B) = 0.24. Are events A and B independent?
a. Yes, they are independent
b. No, they are not independent
CQ1) Given P(A) = 0.5; P(B) = 0.7 and P(A and B) = 0.25. Are events A and B independent?
a. Yes, they are independent
b. No, they are not independent
CQ2) What is the probability that a randomly chosen order was completed by Supplier 2?
a)
b)
c)
d)
0.2
0.4
0.6
0.64
Contingency table
Supplier 1
Supplier 2
Total
Defect
No Defect Total
0.16
0.24
0.4
0.2
0.4
0.6
0.36
0.64
1
CQ3) Are defects independent of suppliers?
a. Yes, they are independent
b. No, they are not independent
What do you think about the pace of this course? In your opinion, how are topics covered?
a. Too fast
b. Slightly fast
c. Just right
d. Slightly slow
e. Too Slow
CQ) To find out if its advertising works, a store surveyed some people and collected data on whether
they saw the ad (saw ad, did not see ad), and whether a purchase was made (purchase, no purchase).
Three joint probabilities were calculated as
P(see ad and purchase) = 0.18
P(see ad and no purchase) = 0.42
P(do not see ad and purchase) = 0.12
Are the ads effective? In other words are seeing an ad and purchasing independent?
a.
b.
c.
d.
Yes, they are independent
No, they are not independent
Not enough data
CQ1) Following is the distribution of the number of absent employees per day.
X
0
1
2
3
4
5
6
7
P(x)
.005
.025
.310
.340
.220
.080
.019
.001
What is P(2 &lt; X &lt; 5)?
a)
b)
c)
d)
.340
.560
.870
.950
CQ2) What is the mean number of absent employees per day?
a)
b)
c)
d)
2.758
3.066
3.783
4.125
CQ1) : A small feeder airline knows that the probability is .10 that a reservation holder will not show up
for its daily 7:15 am flight into a hub airport. The flight carries 9 passengers.
If the airline overbooks by selling 10 seats, what is the probability that no one will have to be bumped?
a)
b)
c)
d)
.349
.387
.612
.651
CQ) Most airline flights do not experience any mishandled bags. Some flights will have one
bag lost; a few will have two bags lost; very rarely will a flight lose three bags, and so on. It
is reasonable to assume that the average number of bags lost is 0.3 bags/flight and that the
number of bags lost on a randomly selected flight follows a Poisson distribution. What is
the probability that 2 or more bags are lost on a particular flight?
A. 0.037
B. 0.7408
C. 0.2222
D. 0.9630
CQ1) Find P (-1.4 &lt; Z &lt; 0.6).
a)
b)
c)
d)
0.0808
0.6449
0.7257
0.8065
CQ2) Lifetimes of light bulbs manufactured by a certain company are normally distributed with a mean
of 5100 hours and standard deviation of 200 hours. They are advertised to last for 5000 hours. What is
the probability that a bulb lasts longer than the advertised figure?
a)
b)
c)
d)
.3085
.6915
.7889
.9900
Approximately how many hours do the top 5% of all bulbs last?
CQ1) If arrivals occur at a mean rate of 3.6 events per hour, the exponential
probability of waiting less than 0.5 hours for the next arrival is
a.
.7122
b.
.8105
c.
.8347
d.
.7809
CQ2) If arrivals occur at a mean rate of 2.6 events per minute, the exponential
probability of waiting more than 1.5 minutes for the next arrival is
a.
.0202
b.
.0122
c.
.0535
d.
.9795
Problem 7.77 from text) MBTF = 10,000 hours. What is the probability of failure within the first 10,000
hours?
1) If Z is such that the area under the curve between +z and –z is 0.50, what is the value of z?
2) Final marks in a statistics class are normally distributed with a mean of 70 and a standard
deviation of 10. The professor must convert all marks to letter grades. He decides that he wants
10% A’s, 30% B’s, 40% C’s, 15% D’s and 5% F’s. Find the cutoffs for each letter grade.
CQ1) The shape of the sampling distribution of the sample mean is
a)
b)
c)
d)
Approximately normal for n&gt;= 30
Skewed to the left
Uniform
Indeterminate
CQ2) To estimate the average annual expenses of students on books and class materials a sample of size
36 is taken. The mean is \$850 and the standard deviation is \$54. A 99% confidence interval for the
population mean is
a. \$823.72 to \$876.28
b. \$832.36 to \$867.64
c. \$826.82 to \$873.18
d. \$825.48 to \$874.52
CQ3) A recent poll of 900 voters on early voting (by Gallup) reported that 30% of all voters would vote
early. Determine the 95% Confidence Interval.
CQ1) A poll showed that 48 out of 120 randomly chosen graduates of California medical
schools last year intended to specialize in family practice. What is the width of a 90%
confidence interval for the proportion that plan to specialize in family practice?
a.
&plusmn;.0447
b.
&plusmn;.0736
c.
&plusmn;.0876
d.
&plusmn;.0894
CQ2) A financial institution wishes to estimate the mean balances owed by its credit
card customers. The population standard deviation is estimated to be \$300. If a 99
percent confidence interval is used and an interval of &plusmn; \$75 is desired, how many
cardholders should be sampled?
a.
3382
b.
629
c.
87
d.
107
CQ3) Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising
lab test costs and would like to know what proportion of the positive lab tests
for prostate cancer are actually proven correct through subsequent biopsy.
JBGHI demands a sample large enough to ensure an error of &plusmn; 2% with 90%
confidence. What is the necessary sample size, to be conservative?
a.
4,148
b.
2,401
c.
1,692
d.
1,604
Chapter 9
CQ1)
The owner of a local nightclub has recently surveyed a random sample of n = 300
customers of the club. She would now like to determine whether or not the mean
age of her customers is over 35. If so, she plans to alter the entertainment to appeal
to an older crowd. If not, no entertainment changes will be made. The appropriate
hypotheses to test are:
a. H o :   35 vs. H1 :   35
b. H o :   35 vs. H1 :   35
c. H o : X  35 vs. H1 : X  35
d. H o : X  35 vs. H1 : X  35
b
CQ2) A spouse stated that the average amount of money spent on Christmas gifts for
immediate family members is above \$1200. The correct set of hypotheses is:
a. H 0 :   200 vs. H1 :   1200
b. H 0 :   1200 vs. H1 :   1200
c. H 0 :   1200 vs. H1 :   1200
d. H 0 :   1200 vs. H1 :   1200
c
Problem) Nike has introduced a new golf ball, endorsed by Tiger Woods, and claims that the new ball
will travel further than Titleist golf balls. A low-handicap golfer who currently uses Titleist has observed
that his average drive is 230 yards, with a (population) standard deviation of 10 yards. He hits 100 drives
with the new Nike ball and measures the distances. The average distance was 231.56 yards. Using a
significance of 1%, conduct a hypothesis test of Nike’s claim.
Problem) A television commercial for a toothpaste claims that more than four out of five dentists
recommend the product. A consumer protection group polls 400 dentists and finds that 329 dentists
recommend the product. Can we infer whether the claim is true at 10% level of significance?
Problem) USA Today reported recently that executives spend one hour reading and sending email. A
statistician doubted the report and conducted a survey of his own. A random sample of 162 executives
yielded a mean of 63.7 minutes with a sample standard deviation of 18.94 minutes. Test the alternative
hypothesis that the mean is not one hour at a 5% significance level.
CQ1) Researchers determined that 60 Kleenex tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Kleenex users yielded the following data
on the number of tissues used during a cold: x = 52 and s = 22. Suppose the alternative
we wanted to test was H1 :   60 . Which of the following is true?
a. reject H o if t &gt; 1.6604
b. reject H o if t &lt; - 1.6604
c. reject H o if t &gt; 1.9842 or Z &lt; - 1.9842
d. reject H o if t &lt; - 1.9842
Problem) A couriers claim that it takes less than 6 hours for delivery is being tested. A sample of 12
deliveries yielded the following delivery times,
3.03
6.33
6.50
5.22
3.56
6.76
7.98
4.82
Is there evidence at the 5% level, to support the courier’s claim?
7.96
4.54
5.09
6.46
NEW FORMULA: A
Formula One Ferrari at
a pit stop during the
Chinese Grand Prix.
In one of the more
unlikely collaborations
of modern medicine,
Britain's largest
children's hospital has
revamped its patient
handoff techniques by
copying the
choreographed pit stops
of Italy's Formula One
Ferrari racing team. The
hospital project has
been in place for two
years and has already
helped reduce the
number of mishaps.
Ferrari
• A Hospital Races to
Learn Lessons of
Ferrari Pit Stop
Page
November 14, 2006 WSJ
Suppose a hospital in the US has adopted these techniques. They’ve studied their surgical handoffs both
before and after using the pit stop techniques. From a sample of 53 handoffs prior to changes they
found there were 20 handoffs with technical errors. From a sample of 65 handoffs after the changes
they found there were 18 handoffs with technical errors. Has the proportion of handoffs with technical
errors decreased since the changes?
Suppose the sample sizes were actually 530 and 650 and the sample proportions stayed the same.
Which do you believe would be most likely?
A)
B)
The p-value would drop significantly allowing us to reject the null hypothesis.
There would be no change in the result of the hypothesis test.
Consider this same hospital. In addition to tracking handoff errors, the hospital also tracks handoff
time. In these same samples, the average handoff time before changes was 23 minutes with a
standard deviation of 5 minutes. After the changes, the average handoff time was 15 minutes with a
standard deviation of 8 minutes. Recall that the sample sizes were 53 and 65, respectively. Has there
been a significant reduction in average handoff time?
The manufacturer of an MP3 Player wanted to know whether a 10% reduction in price is enough to
increase the sales of their product. To investigate, the owner randomly selected seven outlets and
collected sales data from the month of February. For the month of March the MP3 player sold at the
reduced price. Reported below are the number of units sold at each of the outlets for February and
March. At the .10 level of significance, can the manufacturer conclude that the price reduction resulted
in an increase in sales?
Sales
Feb
138
121
88
115
141
125
96
March
128
134
152
135
134
126
112
Random samples of Tuesday and Friday withdrawals from a college-campus ATM were compared to see
whether or not there was a difference in the means.
Friday: 82.40, 75.35,25
Tuesday: 41.00, 35.23, 20
CQ) A regression analysis between Mileage (dependent variable in miles per gallon) and Speed
(independent variable in mph) yielded the least squares regression line ŷ  50.6563 –
0.3531x. What is the gas mileage of a car traveling at 70 mph.
a.
25.94
b.
26.87
c.
31.25
d.
32.49
Chi-Square test of Independence
Problem 1)
Republicans
Democrats
Independent
Against
For Bailout
Bailout
27
33
10
29
21
20
Problem 2)
Close Gay
Friend or
Family
Allowed to
Marry
Should Not be
Allowed to
marry
No Close Gay
Friend or
Family
67
19
32
62
Chi-Square test for the goodness of fit
A statistics professor posted the following grade distribution guidelines for his elementary
statistics class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary
statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs.
Test at the 5% significance level to determine whether the actual grades deviate
significantly from the posted grade distribution guidelines.
```