(a)
The
(a)
Answer to Problem 5E
The probability for
Explanation of Solution
Given info:
The value of binomial random variable X is 18 with
Calculations:
Binomial Distribution:
A random variable X is said to follow Binomial distribution if X has only two outcomes “success” and “failure” and the mass
Where n is the number of trials and p is the probability of success,
The mean is
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
The z-score value is defined as
The mean of binomial distribution is
The standard deviation of binomial distribution is
The formula for finding the z score is,
Substitute 18 for x, 15 for
The probability that 65 to 85 (inclusive) of them live in homes that they own is,
The z score is obtained as follows:
For
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 0.0 and Standard deviation as 1.0.
- Click the Shaded Area tab.
- Choose X value and Middle for the region of the curve to shade.
- Enter the X value1 as -5.26.
- Enter the X value2 as -4.89.
- Click OK.
Output using the MINITAB software is given below:
From MINITAB output,
Thus, the probability for
(b)
The probability for
(b)
Answer to Problem 5E
The probability for
Explanation of Solution
Given info:
The value of binomial random variable X is 44 with
Calculations:
The mean of binomial distribution is
The standard deviation of binomial distribution is
The formula for finding the z score is,
Substitute 44 for x, 40 for
Software procedure:
Step-by-step procedure to obtain the probability using the MINITAB software:
- Choose Calc > Probability Distributions > Normal Distribution.
- Choose Probability.
- In Mean, enter 0.
- In Standard deviation, enter 1.0.
- In Input constant, enter 1.42.
- Click OK.
Output using the MINITAB software is given below:
From MINITAB output,
Thus, the probability for
(c)
The probability for
(c)
Answer to Problem 5E
The probability for
Explanation of Solution
Given info:
The value of binomial random variable X is 12 with
Calculations:
The mean of binomial distribution is
The standard deviation of binomial distribution is
The formula for finding the z score is,
Substitute 12 for x, 10 for
Software procedure:
Step-by-step procedure to obtain the probability using the MINITAB software:
- Choose Calc > Probability Distributions > Normal Distribution.
- Choose Probability.
- In Mean, enter 0.
- In Standard deviation, enter 1.0.
- In Input constant, enter 0.67.
- Click OK.
Output using the MINITAB software is given below:
From MINITAB output,
Thus, the probability for
Want to see more full solutions like this?
Chapter 6 Solutions
Elementary Statistics: A Step-by-Step Approach with Formula Card
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman