Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 6, Problem 6.57SE
a.
To determine
To find:The value of
b.
To determine
To find: The value of
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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 6 Solutions
Introduction to Probability and Statistics
Ch. 6.3 - Consider a standard normal random variable with =0...Ch. 6.3 - Find these probabilities associated with the...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Calculate the area under the standard normal curve...Ch. 6.3 - Find the following probabilities for the standard...Ch. 6.3 - Find these probabilities for the standard normal...Ch. 6.3 - a. Find a z0 such that P(zz0)=.025 . b. Find a z0...Ch. 6.3 - Prob. 6.8ECh. 6.3 - Prob. 6.9ECh. 6.3 - a. Find a z0 such that P(z0zz0)=.90 . b. Find a z0...
Ch. 6.3 - Find the following percentiles for the standard...Ch. 6.3 - A normal random variable x has mean =10 and...Ch. 6.3 - Prob. 6.13ECh. 6.3 - Prob. 6.14ECh. 6.3 - A normal random variable x has mean 35 and...Ch. 6.3 - Prob. 6.16ECh. 6.3 - A normal random variable x has an unknown mean and...Ch. 6.3 - Hamburger Meat The meat department at a local...Ch. 6.3 - Human Heights Human heights are one of many...Ch. 6.3 - Christmas Trees The diameters of Douglas firs...Ch. 6.3 - Cerebral Blood Flow Cerebral blood flow (CBF) in...Ch. 6.3 - Braking Distances For a car traveling 30 miles per...Ch. 6.3 - Elevator Capacities Suppose that you must...Ch. 6.3 - Sunflowers An experimenter publishing in the...Ch. 6.3 - Prob. 6.26ECh. 6.3 - Prob. 6.27ECh. 6.3 - Prob. 6.28ECh. 6.3 - Prob. 6.30ECh. 6.3 - How Many Words? A publisher has discovered that...Ch. 6.3 - Prob. 6.32ECh. 6.4 - Consider a binomial random variable x with n=25...Ch. 6.4 - Prob. 6.36ECh. 6.4 - Prob. 6.37ECh. 6.4 - Let x be a binomial random variable with n=15 and...Ch. 6.4 - Let x be a binomial random variable with n=100 and...Ch. 6.4 - Prob. 6.40ECh. 6.4 - Prob. 6.41ECh. 6.4 - Prob. 6.42ECh. 6.4 - Prob. 6.43ECh. 6.4 - Prob. 6.44ECh. 6.4 - Prob. 6.45ECh. 6.4 - Prob. 6.46ECh. 6.4 - No Shows Airlines and hotels often grant...Ch. 6.4 - Prob. 6.49ECh. 6.4 - Pepsi’s Market Share Two of the biggest soft drink...Ch. 6.4 - Prob. 6.52ECh. 6.4 - Prob. 6.53ECh. 6 - Prob. 6.54SECh. 6 - Prob. 6.55SECh. 6 - Prob. 6.56SECh. 6 - Prob. 6.57SECh. 6 - a. Find a z0 such that P(z0zz0)=.95 . b. Find a z0...Ch. 6 - Prob. 6.59SECh. 6 - Let x be a binomial random variable with n=36 and...Ch. 6 - Prob. 6.61SECh. 6 - Prob. 6.62SECh. 6 - Prob. 6.63SECh. 6 - Prob. 6.64SECh. 6 - Prob. 6.65SECh. 6 - Prob. 6.66SECh. 6 - Prob. 6.67SECh. 6 - Prob. 6.68SECh. 6 - Prob. 6.69SECh. 6 - Used Cars A used-car dealership has found that the...Ch. 6 - Washers The life span of a type of automatic...Ch. 6 - Prob. 6.74SECh. 6 - Prob. 6.75SECh. 6 - Prob. 6.77SECh. 6 - Prob. 6.78SECh. 6 - Prob. 6.79SECh. 6 - Prob. 6.80SECh. 6 - No Shows An airline finds that 5% of the persons...Ch. 6 - Prob. 6.82SECh. 6 - Plant Genetics In Exercise 5.75, a cross between...Ch. 6 - Prob. 6.84SECh. 6 - Prob. 6.86SECh. 6 - Prob. 6.87SECh. 6 - Introvert or Extrovert? A psychological...Ch. 6 - Normal Distribution? The chest measurements for...Ch. 6 - Prob. 6.91SECh. 6 - Prob. 6.92SECh. 6 - Prob. 6.93SECh. 6 - Prob. 6.94SECh. 6 - Prob. 6.95SECh. 6 - Prob. 6.96SECh. 6 - Prob. 6.97SE
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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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