ELEMENTARY STATISTICS W/CONNECT >IP<
ELEMENTARY STATISTICS W/CONNECT >IP<
4th Edition
ISBN: 9781259746826
Author: Bluman
Publisher: MCG
Question
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Chapter 6.2, Problem 15E

a.

To determine

To find: The probability that more than 100,000 jobs are available for RNs.

a.

Expert Solution
Check Mark

Answer to Problem 15E

The probability that More than 100,000 jobs are available for RNs is 0.6862.

Explanation of Solution

Given info:

The annual number of jobs for registered nurses follow a normal distribution with mean 103,900 and standard deviation 8,040.

Calculations:

Normal distribution:

A random variable x is said to follow a Normal distribution, if the probability distribution is

f(x)=1σ2πe12(xuσ)2

Where,

μ=Mean of normal variable X

σ=Standard deviation of normal variable X.

π = 3.1415....

e= 2.71828

Standard Normal Distribution:

A Random variable z is said to a standard normal variable if z follows normal distribution with mean μ=0 and variance σ2=1.

Consider a random variable X define as the number of jobs available for registered nurses.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 103,900 and Standard deviation as 8,040.
  • Click the Shaded Area tab.
  • Choose X value and Right Tail for the region of the curve to shade.
  • Enter the X value as 100,000.
  • Click OK.

Output using the MINITAB software is given below:

ELEMENTARY STATISTICS W/CONNECT >IP<, Chapter 6.2, Problem 15E , additional homework tip  1

From MINITAB, the probability that More than 100,000 jobs are available for RNs is 0.6862.

b.

To determine

To find: The probability that more than 80,000 but less than 95,000 jobs are available for RNs.

b.

Expert Solution
Check Mark

Answer to Problem 15E

The probability that more than 80,000 but less than 95,000 jobs are available for RNs is 0.1327.

Explanation of Solution

Calculations:

Normal distribution:

A random variable x is said to follow a Normal distribution, if the probability distribution is

f(x)=1σ2πe12(xuσ)2

Where,

μ=Mean of normal variable X

σ=Standard deviation of normal variable X.

π = 3.1415....

e= 2.71828

Standard Normal Distribution:

A Random variable z is said to a standard normal variable if z follows normal distribution with mean μ=0 and variance σ2=1.

Consider a random variable X define as the number of jobs available for registered nurses.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 103,900 and Standard deviation as 8,040.
  • Click the Shaded Area tab.
  • Choose X value and Both Tail for the region of the curve to shade.
  • Enter the X value 1 as 80,000.
  • Enter the X value 2 as 95,000.
  • Click OK.

Output using the MINITAB software is given below:

ELEMENTARY STATISTICS W/CONNECT >IP<, Chapter 6.2, Problem 15E , additional homework tip  2

From MINITAB, the probability that more than 80,000 but less than 95,000 jobs are available for RNs is 0.1327.

c.

To determine

To find: The value if the probability is 0.1977 that more than X amount of jobs are available.

c.

Expert Solution
Check Mark

Answer to Problem 15E

The required X-value is 110,733.

Explanation of Solution

Calculations:

Normal distribution:

A random variable x is said to follow a Normal distribution, if the probability distribution is

f(x)=1σ2πe12(xuσ)2

Where,

μ=Mean of normal variable X

σ=Standard deviation of normal variable X.

π = 3.1415....

e= 2.71828

Standard Normal Distribution:

A Random variable z is said to a standard normal variable if z follows normal distribution with mean μ=0 and variance σ2=1.

Consider a random variable X define as the number of jobs available for registered nurses.

Software procedure:

Step-by-step procedure to obtain the probability using the MINITAB software:

  • Choose Graph > Probability Distribution Plot choose View Probability> OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 103,900 and Standard deviation as 8,040.
  • Click the Shaded Area tab.
  • Choose X value and Both Tail for the region of the curve to shade.
  • Enter the X value 1 as 80,000.
  • Enter the X value 2 as 95,000.
  • Click OK.

Output using the MINITAB software is given below:

ELEMENTARY STATISTICS W/CONNECT >IP<, Chapter 6.2, Problem 15E , additional homework tip  3

From MINITAB, the required X-value is 110,733.

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Chapter 6 Solutions

ELEMENTARY STATISTICS W/CONNECT >IP<

Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 11ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 13ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 17ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 21ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 23ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 27ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 29ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 31ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 33ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 37ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - Find the z value to the left of the mean so that...Ch. 6.1 - Find the z value to the right of the mean so that...Ch. 6.1 - Find two z values, one positive and one negative,...Ch. 6.1 - 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Prob. 15ECh. 6.2 - Salary of Full Professors The average salary of a...Ch. 6.2 - Prob. 17ECh. 6.2 - Itemized Charitable Contributions The average...Ch. 6.2 - New Home Sizes A contractor decided to build homes...Ch. 6.2 - New-Home Prices If the average price of a new...Ch. 6.2 - Cost of Personal Computers The average price of a...Ch. 6.2 - Reading Improvement Program To help students...Ch. 6.2 - Prob. 23ECh. 6.2 - Ages of Amtrak Passenger Cars The average age of...Ch. 6.2 - Lengths of Hospital Stays The average length of a...Ch. 6.2 - High School Competency Test A mandatory competency...Ch. 6.2 - Product Marketing An advertising company plans to...Ch. 6.2 - Prob. 28ECh. 6.2 - Wristwatch Lifetimes The mean lifetime of a...Ch. 6.2 - Police Academy Acceptance Exams To qualify for a...Ch. 6.2 - In the distributions shown, state the mean and...Ch. 6.2 - SAT Scores Suppose that the mathematics SAT scores...Ch. 6.2 - Prob. 33ECh. 6.2 - Standardizing If a distribution of raw scores were...Ch. 6.2 - 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