
Concept explainers
Find the
a. n = 1000, p = 0.1
b. n = 500, p = 0.25 125;
c. n = 50, p = ⅖
d. n = 36, p =
a.

To calculate: The mean, variance and standard deviation.
Answer to Problem 18E
The mean is 100.
The variance is 90.
The standard deviation is 9.487.
Explanation of Solution
Given info:
The number of trials n is 1,000 andp is 0.01.
Calculation:
Mean of binomial distribution:
Where, n is the number of trials and p is the probability of success.
Substitute n as 10 and p as 0.1
Thus, the mean is 100.
Variance of binomial distribution:
Where, n is the number of trials and p is the probability of success and q is
Substitute n as 10, p as 0.1 and q as
Thus, the variance is 90.
Standard deviation:
Substitute n as 10, p as 0.1 and q as
Thus, the standard deviation is 9.487.
b.

To calculate: The mean, variance and standard deviation.
Answer to Problem 18E
The mean is 125.
The variance is 93.75.
The standard deviation is 9.682.
Explanation of Solution
Given info:
The number of trials n is 500, and p is 0.25.
Calculation:
Mean of binomial distribution:
Where, n is the number of trials and p is the probability of success.
Substitute n as 500 and p as 0.25
Thus, the mean is 125.
Variance of binomial distribution:
Where, n is the number of trials and p is the probability of success and q is
Substitute n as 500, p as 0.25 and q as
Thus, the variance is 93.75.
Standard deviation:
Substitute n as 500, p as 0.25 and q as
Thus, the standard deviation is 9.682.
c.

To calculate: The mean, variance and standard deviation.
Answer to Problem 18E
The mean is 20.
The variance is 4.8.
The standard deviation is 2.191.
Explanation of Solution
Given info:
The number of trials n is 50, and p is
Calculation:
Mean of binomial distribution:
Where, n is the number of trials and p is the probability of success.
Substitute n as 50 and p as
Thus, the mean is 20.
Variance of binomial distribution:
Where, n is the number of trials and p is the probability of success and q is
Substitute n as 50, p as
Thus, the variance is 4.8.
Standard deviation:
Substitute n as 50, p as
Thus, the standard deviation is 2.191.
d.

To calculate: The mean, variance and standard deviation.
Answer to Problem 18E
The mean is 6.
The variance is 5.008.
The standard deviation is 2.238.
Explanation of Solution
Given info:
The number of trials n is 36, and p is
Calculation:
The number of trials is 36 and it is fixed. Also, the probability of success
Mean of binomial distribution:
Where, n is the number of trials and p is the probability of success.
Substitute n as 36 and p as
Thus, the mean is 6.
Variance of binomial distribution:
Where, n is the number of trials and p is the probability of success and q is
Substitute n as 6, p as
Thus, the variance is 5.008.
Standard deviation:
Substitute n as 6, p as
Thus, the standard deviation is 2.238.
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Chapter 5 Solutions
Elementary Statistics: A Step By Step Approach
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