Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 1, Problem 1.65SE
To determine
To find: The appropriate graph for the data.
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Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
1.What percent of the refunds are more than $3,500?
2. What percent of the refunds are more than $3500 but less than $3579?
3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
Chapter 1 Solutions
Introduction to Probability and Statistics
Ch. 1.3 - Experimental Units Identify the experimental units...Ch. 1.3 - Qualitative or Quantitative? Identify each...Ch. 1.3 - Discrete or Continuous? Identify the following...Ch. 1.3 - Discrete or Continuous? Identify each quantitaive...Ch. 1.3 - Parking on Campus Six vehicles are selected from...Ch. 1.3 - Past U.S. Presidents A data set consists of the...Ch. 1.3 - Voter Attitudes You are a candidate for your state...Ch. 1.3 - Cancer Survival Times A medical researcher wants...Ch. 1.3 - New Teaching Methods An educational researcher...Ch. 1.3 - Fifty people are grouped into four categrires A,...
Ch. 1.3 - Jeans A manufacturer of jeans has plants in...Ch. 1.3 - Prob. 1.12ECh. 1.3 - Want to Be President? Would you want to be the...Ch. 1.3 - Facebook Fanatics The social networking site...Ch. 1.3 - Back to Work How long does it take you to adjust...Ch. 1.5 - Construct a stem and leaf plot for these 50...Ch. 1.5 - Refer to Exercise 1.16. Construct a relative...Ch. 1.5 - Prob. 1.18ECh. 1.5 - A discrete variable can take on oniy the values 0....Ch. 1.5 - Prob. 1.20ECh. 1.5 - Prob. 1.21ECh. 1.5 - Prob. 1.22ECh. 1.5 - Cheeseburgers Create a dotplot for the number of...Ch. 1.5 - Prob. 1.24ECh. 1.5 - Prob. 1.25ECh. 1.5 - Prob. 1.26ECh. 1.5 - Education Pays Off! Education pays off, according...Ch. 1.5 - Preschool The ages (in months) at which 50...Ch. 1.5 - Prob. 1.29ECh. 1.5 - Prob. 1.30ECh. 1.5 - Prob. 1.31ECh. 1.5 - Prob. 1.32ECh. 1.5 - Prob. 1.33ECh. 1.5 - RBC Counts The red blood cell count of a healthy...Ch. 1.5 - Prob. 1.35ECh. 1.5 - Prob. 1.36ECh. 1.5 - Hazardous Waste How safe is your neighborhood? Are...Ch. 1 - Quantitative or Qualitative? Identify each...Ch. 1 - Symmetric or Skewed? Do you expect the...Ch. 1 - Continuous or Discrete? Identify each variable as...Ch. 1 - Prob. 1.41SECh. 1 - Continuous or Discrete, again Identify each...Ch. 1 - Aqua Running Aqua running has been suggested as a...Ch. 1 - Prob. 1.44SECh. 1 - Ages of Pennies We collected 50 pennies and...Ch. 1 - Prob. 1.46SECh. 1 - Presidential Vetoes Here is a list of the 44...Ch. 1 - Prob. 1.48SECh. 1 - Prob. 1.49SECh. 1 - Prob. 1.50SECh. 1 - Prob. 1.51SECh. 1 - Prob. 1.52SECh. 1 - Prob. 1.53SECh. 1 - Student Heights The self-reported heights of 105...Ch. 1 - Prob. 1.55SECh. 1 - Pulse Rates A group of 50 biomedical students...Ch. 1 - Prob. 1.57SECh. 1 - Prob. 1.58SECh. 1 - Prob. 1.59SECh. 1 - Prob. 1.60SECh. 1 - Prob. 1.61SECh. 1 - Old Faithful The data below are the wailing times...Ch. 1 - Prob. 1.63SECh. 1 - Prob. 1.64SECh. 1 - Prob. 1.65SECh. 1 - The number of Starhucks coffee shops in cities...Ch. 1 - What’s Normal? The 98.6 degree standard for human...
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- In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forwardProblem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forward
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