Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 5, Problem 5.63SE
(a)
To determine
To use the formula for the binomial
(b)
To determine
To construct a probability distribution.
(c)
To determine
To find the
(d)
To determine
To find the fraction of the population measurements lying within one standard deviation of the mean by using part (b) and verify the results with Tchebysheff’s Theorem and
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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 5 Solutions
Introduction to Probability and Statistics
Ch. 5.2 - O Canada! The National Hockey League (NHL) has 80%...Ch. 5.2 - Prob. 5.28ECh. 5.2 - Whitefly Infestation Suppose that 10% of the...Ch. 5.2 - Color Preferences in Mice In a psychology...Ch. 5.2 - Back Pain Six in 10 aduts say lower back pain...Ch. 5.2 - Prob. 5.32ECh. 5.2 - Prob. 5.33ECh. 5.2 - Man’s Best Friend According to the Humane Society...Ch. 5.3 - Consider a Poission random variable with =2.5. Use...Ch. 5.3 - Consider a Poission random variable with =3. Use...
Ch. 5.3 - Consider a Poission random variable with =3. Use...Ch. 5.3 - Consider a Poission random variable with =0.8. Use...Ch. 5.3 - Let x be a Poisson random variable with mean =2....Ch. 5.3 - Prob. 5.40ECh. 5.3 - Prob. 5.41ECh. 5.3 - Prob. 5.42ECh. 5.3 - Prob. 5.46ECh. 5.3 - Prob. 5.48ECh. 5.4 - Prob. 5.49ECh. 5.4 - Let x be the number of successes observed in a...Ch. 5.4 - Prob. 5.51ECh. 5.4 - Prob. 5.52ECh. 5.4 - Prob. 5.53ECh. 5.4 - Candy Choices A candy dish contains five blue and...Ch. 5.4 - Defective Computer Chips A piece of electronic...Ch. 5.4 - Gender Bias? A company has lIve applicants for two...Ch. 5 - Prob. 5.59SECh. 5 - Under what conditions can the Poisson random...Ch. 5 - Prob. 5.61SECh. 5 - Tossing a Coin A balanced coin is tossed three...Ch. 5 - Prob. 5.63SECh. 5 - Cancer Survivor Rates The 10-year survival rate...Ch. 5 - Prob. 5.65SECh. 5 - Prob. 5.66SECh. 5 - Prob. 5.67SECh. 5 - Prob. 5.68SECh. 5 - Psychosomatic Problems A psychiatrist believesthat...Ch. 5 - Prob. 5.75SECh. 5 - Prob. 5.77SECh. 5 - Prob. 5.78SECh. 5 - Prob. 5.79SECh. 5 - Dark Chocolate Despite reports that dark chocolate...Ch. 5 - Prob. 5.81SECh. 5 - Prob. 5.82SECh. 5 - Prob. 5.85SECh. 5 - Prob. 5.90SECh. 5 - Earthquakes! Suppose that one out of every 10...Ch. 5 - Prob. 5.92SECh. 5 - Prob. 5.94SECh. 5 - Prob. 5.95SECh. 5 - Prob. 5.96SECh. 5 - Prob. 5.97SECh. 5 - Prob. 5.98SECh. 5 - McDonald’s or Burger King? Suppose that 50% of all...Ch. 5 - Prob. 5.100SE
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