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a.
To find: The
a.
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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
Calculations:
Normal distribution:
A random variable x is said to follow a Normal distribution, if the probability distribution is
Where,
Standard Normal Distribution:
A Random variable z is said to a standard normal variable if z follows normal distribution with mean
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:
From MINITAB, the probability that More than 100,000 jobs are available for RNs is 0.6862.
b.
To find: The probability that more than 80,000 but less than 95,000 jobs are available for RNs.
b.
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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
Where,
Standard Normal Distribution:
A Random variable z is said to a standard normal variable if z follows normal distribution with mean
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:
From MINITAB, the probability that more than 80,000 but less than 95,000 jobs are available for RNs is 0.1327.
c.
To find: The Xvalue if the probability is 0.1977 that more than X amount of jobs are available.
c.
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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
Where,
Standard Normal Distribution:
A Random variable z is said to a standard normal variable if z follows normal distribution with mean
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:
From MINITAB, the required X-value is 110,733.
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Chapter 6 Solutions
ELEMENTARY STATISTICS W/CONNECT >IP<
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