Download Review for test I

Review for test I
Part A
1. You want to buy a fuel efficient hybrid, but you do not know if the new technology is reliable yet.
A Consumer Report article list the average repair cost over five years of ownership as $658 with a
standard deviation of $85.50. If you decide that the maximum amount of money that you can
afford to spend over the five years on repairs is $1000, is the hybrid a safe buy? Explain.
2. We are interested in the TV viewing habits of the country. A sample of Americans is surveyed
and the average amount of time spent watching TV is found to be 4.6 hours per day. Is this
average a population parameter or a sample statistic?
3. A statistics class consists of 24 students who are either unemployed or who are working in lowpaying part-time jobs. The class also includes a professor who is paid an enormous salary (I
wish). Would it be better to use the mean, median, or the mode to describe the earnings of the
typical person in the class of 25 people?
4. The average of a set of data points is 13.5, and the median of the same data set is 8.2. Is the
distribution skewed? If so, is it right or left skewed?
5. Which do you think has more variation: the IQ scores of the 22 statistic professors for FIU or the
IQ scores of 22 patrons watching a movie?
6. The average human can run at a maximum short distance speed of 22 miles per hour with a
standard deviation of 2 miles per hour. A runner from Kenya was recently clocked at a speed of
27.89 while running the 100yrd dash. Is this speed considered unusually fast for a human being?
Explain your answer assuming 27.89 was his maximum speed.
7. Which test result is relatively better: an 85 on a psychology exam or a 45 on an economics exam?
The psychology exam has a mean of 90 and a standard deviation of 10, and the economics exam
has a mean of 55 and a standard deviation of 5?
8. The wife of a farmer in a small rural town of 1050 people wishes to open a small video rental store.
Before doing so, she would like to estimate the number of people in that town who would be interested
in renting videos. Over the course of one week, she decides to ask 50 people randomly at a local post
office whether or not they would rent videos.
a. What is the population of interest?
b. What is the population sampled from?
c. Identify the variable of interest.
9. Suppose a light bulb manufacturer claims that the mean lifetime of its bulbs is 35 hours. Assume
you have prior knowledge that the bulb lifetimes have mound shaped distribution with a standard
deviation of 5 hours.
a.) If the manufacturer's claim is true, approximately what percent of light bulbs will burn out in less
than 20 hours?
b.) Suppose you randomly select one of the bulbs and it burns out in less than 20 hours. Do you suspect
the manufacturer's claim is incorrect? EXPLAIN.
c.) What percentage of bulbs can be expected to burn out between 30 and 45 hours?
10. A professor believes that if a class is allowed to work on an examination as long as desired, the
times spent by the students would be approximately mound shaped with a mean of 40 minutes and a
standard deviation of 6 minutes. Approximately how long should be allotted for the examination if the
professor wants almost all, say 97.5%, of the class to finish?
Part 2
1.While eating in FIU cafeteria, 200 students are asked to perform a taste test in which they drink from
two unmarked cups. They are then asked which drink they prefer. Identify the variable of interest,
the data collection method, type of the data, and population of interest to the cafeteria administration.
2. Standard deck of card contains 52 cards. Find the probability of:
a) Selecting a spade card
b) Getting a king or a jack
c) Choosing a red card or a queen
d) If 3 cards are selected without replacement find the probability all three are aces?
e) If 3 cards are selected without replacement find the probability of at least one diamond card?
3. Given a sample: 33, 24, 21, 14, 24.
Calculate the variance, S.D., mean, median, mode, range.
4. For each variable described, indicate whether it is nominal, ordinal, discrete or continuous.
____ 1) the number of errors in a one-page letter
___ 2) the brand of jeans preferred by a student
___ 3) the educational level of a child’s mother
___4) the weight of the meat in a chef’s salad
5. A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A
walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV
ad or were referred to the salon (but not both). The results follow
Not Satisfied
Neutral
Walk In
21
18
TV Ad
9
25
Referred
5
37
Total
35
80
Satisfied
Very Satisfied
Total
36
28
103
43
31
108
Find the probability that a customer is: a ) Not satisfied
59
48
149
138
107
360
b) Very satisfied, given referred
c) At least satisfied and TV Ad
d) Are the events (A) satisfied and (B) referred independent or not? Prove your answer.
6. Suppose the average height and S.D. of 50 students in a class are 66 inch and 3 inch respectively.
a) If nothing is known about the shape of the distribution, what proportion represents the number of students
outside the interval from 60 to 72 inch?
b) If the heights have a mound shaped and symmetric histogram, what
proportion of the observations will be less than 57 inch?
c) If the heights have a mound shaped and symmetric histogram, what proportion of the students will be
less than 60 and more than 69 inch?
d) If nothing is known about the shape of the distribution, give an interval that will contain the heights of
at least 8/9 of the class.
7). A study was conducted to study the customer satisfaction levels for one overnight shipping business.
In addition to the customer’s satisfaction level, the customers were asked how often they used
overnight shipping. The results are shown below in the following table:
Frequancy of use
< 2 per month
2 – 5 per month
5 per month
Total
High
250
140
70
460
Satisfaction Level
Medium
Low
140
10
55
5
25
5
220
20
Total
400
200
100
700
(a) What proportion of the respondents did not have a high level of satisfaction with the company?
(b) What proportion of the customers were highly satisfied with the company and used the
company greater than 5 times per month?
(c) What proportion of the customers had a low level of satisfaction with the service or used the
company between 2 and 5 times per month?
(d) Given that a customer uses the company less than 2 times per month, find the probability that
this customer has a medium level of satisfaction with the service.
8. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results
of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house
using gas or electric energy had a mean of $121 and a standard deviation of $13. If nothing is known about
the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $95?
9. By law, a box of cereal labeled as containing 16 ounces must contain at least 16 ounces of cereal. It is
known that the machine filling the boxes produces a distribution of fill weights that is mound-shaped,
with mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To
ensure that most of the boxes contain at least 16 ounces, the machine is set so that the mean fill per box is
16.09 ounces. What percentage of the boxes do, in fact, contain at least 16 ounces?
10. Luke took a test and scored in the 88th percentile. What percentage of the scores were above his score?
11. A random sample of 30 receipts for individuals shopping at the Community Drug Store showed the
sample mean to be x = $28.19 with sample standard deviation s = $4.06. Use Chebyshev’s Theorem to find
the smallest interval centered on the mean in which we can expect at least 88.9% of the data to fall.
12. In Chemistry 400, weights are assigned to required activities as follows:
class participation - 15%; exam 1 - 20%; exam 2 - 20%; exam 3 - 20%; laboratory - 25%.
Each activity is graded on a 100 point scale. Mary earned 70 points on class participation, 80 points
on exam 1, 64 points on exam 2, 77 points on exam 3, and 96 points on laboratory. Compute her
overall weighted average in the Chemistry 400 class.
13. Choose the highest level of measurement for variable
A.
B.
C.
D.
E.
Temperature of refrigerators (in degrees Celsius).
Horsepower of racecar engines
Marital status of school board members
Ratings of television programs (poor, fair, good, excellent)
Ages of children enrolled in a daycare
14. Consider the four following statements and identify the one that is a statistical inferential statement:
a) Many people agree that the government should do something to reduce taxes.
b) According to the last Human Resource Office Report, 40% of the faculty at O’Connor College consists of
adjunct professors.
c) Based on a sample survey, where 500 businessmen were interviewed, a study concluded that 78% of
Executives of international companies prefer water to soft drink during their flights.
d) The number 28 is a multiple of seven. The number 56 is its double. Then the number 56 is a multiple of 7.
15. Consider the following statements about measures. Identify the measure as ”parameter” or “statistic”
a) A sample survey among working women revealed that 78% prefer man doctors _________________
b) Two third of the students in Broward college, registered on line this summer _________________
16. A consumer research company wants to estimate the average cost of an airline ticket for a round
trip within the continental United States. A random sample of 50 airfares was gathered giving an
average price of $438. Identify the variable.
(a) Random sample of 50 airfares (b) Airline fare
(c) Consumer research company (d) Quantitative (e) $438
17. The delivery time for a package sent within the United States is bell-shaped distributed
with mean of 4 days and standard deviation of approximately 1 day. If 300 packages
are being sent, how many packages will arrive in less than 3 days?
(a) 8
(b) 96
(c) 102
(d) 198
(e) 48
18. Suppose P(A)=.4, P(B)=.3 and P(AUB)=.60.
Find P(AB) and check whether events A and B are independent.
19. A manufacturer of 35-mm cameras knows that a shipment of 50 cameras sent to a large discount
store contains 5 defective cameras. The manufacturer also knows that the store will choose three of the
cameras at random, test them, and accept the shipment if neither is defective. What is the probability
that the shipment is accepted?
20. Suppose a basketball player is an excellent free throw shooter and makes 83% of his free throws.
Assume that free throw shots are independent of one another. Suppose this player gets to shoot four free
throws. Find the probability that he misses at least one of all three consecutive free throws.
21. Suppose, at FIU the µ and σ of all students cumulative GPAs, are 2.5 and 0.5, respectively. The
president of FIU wishes to graduate the top 2.5% of the students with cum laude honors and the top
.15% with summa cum laude honors. Assume that distribution for the GPAs scores is mound shaped
and symmetric.
Where should be the limits be set in terms of GPAs?
In terms of percentile scores?
22. Time to take standardized Exam is known to have mound shaped and symmetric distribution with
σ = 10 min and P2.5 = 55 min. How much time will it take for 50% of the entire class to finish this Exam?