
a.
To find:
The first and third

Answer to Problem 16CR
Solution:
The first quartile is
Explanation of Solution
Given:
In statistics, a measurable
The normal (also known as Gaussian or Gauss-Laplacian) distribution is the most prevalent continuous
Where,
The normal Gaussian distribution with the following characteristics:
is called standard normal distribution.
The appropriate probability density function transforms to
A normal distribution can be converted to standard normal distribution by defining the
Where
The first quartile is defined as the middle point between smallest numbers and median that has the
The third quartile is defined as the mid-point between median and largest number that has
Initially, the
Calculation:
The first quartile is obtained at the position in the table where the value is 0.25 as:
Whose equivalent
The third quartile is obtained at the position in the table where the value is 0.75 as:
Whose equivalent
Conclusion:
The first quartile is
b.
To find:
Value of the mean and third quartile for given standard deviation and first quartile.

Answer to Problem 16CR
Solution:
The value of the mean is
Explanation of Solution
Given:
First quartile
Description:
In statistics, a measurable function that is used to represent outcomes or occurrences of random phenomenon as real numbers is defined as a random variable.
The normal (also known as Gaussian or Gauss-Laplacian) distribution is the most prevalent continuous probability distribution function and the real world hosts a milieu of the variables that are normally distributed and the probability density function is given by:
where,
The normal Gaussian distribution with the following characteristics:
The appropriate probability density function transforms to
A normal distribution can be converted to standard normal distribution by defining the
where
The first quartile is defined as the middle point between smallest numbers and median that has the
The third quartile is defined as the mid-point between median and largest number that has
Using the first quartile, the corresponding
Thereafter, the third quartile
Calculation:
The
Then, the mean is:
Thereafter, the
Then, the third quartile
Conclusion:
The value of the mean is
c.
To find:
The mean and standard deviation for given data.

Answer to Problem 16CR
Solution:
The required mean is
Explanation of Solution
Given:
First quartile
Third quartile
Description:
In statistics, a measurable function that is used to represent outcomes or occurrences of random phenomenon as real numbers is defined as a random variable.
The normal (also known as Gaussian or Gauss-Laplacian) distribution is the most prevalent continuous probability distribution function and the real world hosts a milieu of the variables that are normally distributed and the probability density function is given by:
Where,
The normal Gaussian distribution with the following characteristics:
The appropriate probability density function transforms to
A normal distribution can be converted to standard normal distribution by defining the
where
The first quartile is defined as the middle point between smallest numbers and median that has the
The third quartile is defined as the mid-point between median and largest number that has
The
Calculation:
The
Conclusion:
The required mean is
d.
To find:
The values of standard deviation and first quartile for given data.

Answer to Problem 16CR
Solution:
The value of standard deviation is
Explanation of Solution
Given:
Description:
In statistics, a measurable function that is used to represent outcomes or occurrences of random phenomenon as real numbers is defined as a random variable.
The normal (also known as Gaussian or Gauss-Laplacian) distribution is the most prevalent continuous probability distribution function and the real world hosts a milieu of the variables that are normally distributed and the probability density function is given by:
where,
The normal Gaussian distribution with the following characteristics:
is called standard normal distribution.
The appropriate probability density function transforms to
A normal distribution can be converted to standard normal distribution by defining the
where
The first quartile
The third quartile
The relation between first quartile, mean and third quartile is:
The
Since mean and third quartile are given, the first quartile is computed using the relation above.
Calculation:
The
Then, the value of standard deviation is:
Z-score of the first quartile is -0.67
Conclusion:
The value of standard deviation is
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Chapter 6 Solutions
Beginning Statistics, 2nd Edition
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