Statistics
Class Name : MAT2058 Statistics (10wk) – 20200627 – MAT2058 Statistics VB05
Instructor Name : Bibi
Student Name : _____________________ Instructor Note :
Question 1 of 13
There is some evidence that, in the years , a simple name change resulted in a short-term increase in the price of certain business firms’ stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, “Does it pay to change your company’s name? A stock market perspective,” Marketing Science v. , pp. .)
Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about %, with a standard deviation of %. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.
(a) According to Chebyshev’s theorem, at least 84% of the relative increases in stock price lie between _____% and _____%. (Round your answer to 2 decimal places.)
(b) According to Chebyshev’s theorem, at least _____% of the relative increases in stock price lie between 0.49 % and 1.17 %. a. 56% b. 75% c. 84% d. 89%
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the relative increases in stock price lie between 0.49 % and 1.17 %. a. 68% b. 75% c. 95% d. 99.7%
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the relative increases in stock price lie between _____% and _____%.
Question 2 of 13
A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of to . In a
recent year, the national mean score for the writing section was , with a standard deviation of . Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.
(a) According to Chebyshev’s theorem, at least _____% of the scores lie between 26.4 and 70.0 . a. 56% b. 75% c. 84% d. 89%
(b) According to Chebyshev’s theorem, at least _____% of the scores lie between 31.85 and 64.55 . a. 56% b. 75% c. 84% d. 89%
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the scores lie between 26.4 and 70.0 . a. 68% b. 75% c. 95% d. 99.7%
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the scores lie between _____ and _____.
Question 3 of 13
−1981 85
6 −320 35,1987
0.83 0.17
20 80 48.2 10.9
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Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is mmHg, with a standard deviation of mmHg.
Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.
(a) According to Chebyshev’s theorem, at least _____% of the measurements lie between 123.1 mmHg and 146.7 mmHg. a. 56% b. 75% c. 84% d. 89%
(b) According to Chebyshev’s theorem, at least 8/9 (about 89%) of the measurements lie between _____mmHg and _____mmHg. (Round your answer to 1 decimal place.)
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the measurements lie between _____mmHg and _____mmHg.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the measurements lie between 123.1 mmHg and 146.7 mmHg. a. 68% b. 75% c. 95% d. 99.7%
Question 4 of 13
A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was years old, with a standard deviation of years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.
(a) According to Chebyshev’s theorem, at least 84% of the home buyers’ ages lie between _____years and _____years. (Round your answer to the nearest integer.)
(b) According to Chebyshev’s theorem, at least _____% of the home buyers’ ages lie between 27 years and 63 years. a. 56% b. 75% c. 84% d. 89%
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the home buyers’ ages lie between 27 years and 63 years. a. 68% b. 75% c. 95% d. 99.7%
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the home buyers’ ages lie between _____years and _____years.
Question 5 of 13
134.9 5.9
45 9
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Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of “girls” ( ) and “boys” ( ), which we write , , etc. For each outcome, let be the random variable counting the
number of boys in each outcome. For example, if the outcome is , then . Suppose that the random variable
is defined in terms of as follows: . The values of are thus:
Outcome
Value of
Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of .
Then fill in the appropriate probabilities in the second row.
Value of
Question 6 of 13
Fill in the values in the table below to give a legitimate probability distribution for the discrete random variable ,
whose possible values are , , , , and .
Value x of X P( X =x )
-4 0.29
3 0.11
4
5 0.21
6
Question 7 of 13
The ages (in years) of the employees at a particular computer store are the following.
Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
(If necessary, consult a list of formulas.)
Question 8 of 13
Find the standard deviation of this sample of numbers. Round your answer to two decimal places.
(If necessary, consult a list of formulas.)
Question 9 of 13
g b gbg bbb R bgb =R bgb 2
X R =X −R 4 X
bgg ggb bbb bbg bgb gbb gbg ggg
X −3 −3 −1 −2 −2 −2 −3 −4
X pX x X
x X PX x
P =X x X −4 3 4 5 6
6
32, 32, 24, 45, 35, 42
69, 51, 56, 70, 62, 40
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Many tests that purport to measure intelligence are timed. The decision of how much time to allow for such a test often is made after examination of samples of times for completion of practice versions of the test. Below is a histogram summarizing such times for completion for one type of test.
Based on this histogram, estimate the standard deviation of the sample of times.
Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.
(If necessary, consult a list of formulas.)
Question 10 of 13
A major cab company in Chicago has computed its mean fare from O’Hare Airport to the Drake Hotel to be , with a
standard deviation of . Based on this information, complete the following statements about the distribution of the company’s fares from O’Hare Airport to the Drake Hotel.
(a) According to Chebyshev’s theorem, at least _____% of the fares lie between 21.81 dollars and 37.45 dollars. a. 56% b. 75% c. 84% d. 89%
(b) According to Chebyshev’s theorem, at least _____% of the fares lie between 23.765 dollars and 35.495 dollars. a. 56% b. 75% c. 84% d. 89%
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the fares lie between 21.81 dollars and 37.45 dollars. a. 68% b. 75% c. 95% d. 99.7%
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the fares lie between _____dollars and _____dollars.
Question 11 of 13
32
Frequency
Time for completion (in minutes)
15
10
5
0
2
10
14
6
8 12 16 20 24
32
$29.63 $3.91
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Archie is fed up with waiting in line at his local post office and decides to take action. Over the course of the next few months, he records the waiting times for each of a random selection of post office visits made by him and other customers. These waiting times (in minutes) are as follows:
Construct a box-and-whisker plot for the data.
Question 12 of 13
The following are the annual salaries of chief executive officers of major companies. (The salaries are written in thousands of dollars.)
Find th and th percentiles for these salaries.
(If necessary, consult a list of formulas.)
Question 13 of 13
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects Ultra batteries and finds that they have a mean lifetime of hours, with a standard
deviation of hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.
(a) According to Chebyshev’s theorem, at least 36% of the lifetimes lie between _____hours and _____hours. (Round your answer to the nearest integer.)
(b) According to Chebyshev’s theorem, at least _____% of the lifetimes lie between 651 hours and 979 hours. a. 56% b. 75% c. 84% d. 89%
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _____% of the lifetimes lie between 651 hours and 979 hours. a. 68% b. 75% c. 95% d. 99.7%
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the lifetimes lie between _____hours and _____hours.
18
27, 19, 24, 23, 19, 26, 25, 10, 22, 5, 14, 22, 11, 13, 6, 30, 15, 12
17
723, 472, 315, 790, 405, 633, 676, 609, 362, 495, 338, 743, 519, 75, 428, 542, 224
25 70
1000 815 82
5 10 15 20 25
Waiting time (in minutes)
