Concept explainers
a.
Find the value of
a.
Answer to Problem 42E
The value of
Explanation of Solution
Calculation:
The table represents the
From the probability distribution table, the probability at the point
Thus, the value of
b.
Find the probability value,
b.
Answer to Problem 42E
The probability value,
Explanation of Solution
Calculation:
The required probability is the sum of the probabilities at
Substituting the values from the probability distribution table,
Thus, the probability value,
c.
Find the probability that no one is in line.
c.
Answer to Problem 42E
The probability that no one is in line is 0.10.
Explanation of Solution
Calculation:
The probability that no one is in line is the probability at the point
Thus, the probability that no one is in line is 0.10.
d.
Find the probability that at least three people are in line.
d.
Answer to Problem 42E
The probability that at least three people are in line is 0.35.
Explanation of Solution
Calculation:
The probability that at least three people are in line is the sum of the probabilities at
Substituting the values from the probability distribution table,
Thus, the probability that at least three people are in line is 0.35.
e.
Find the mean.
e.
Answer to Problem 42E
The mean value is 2.10.
Explanation of Solution
Calculation:
The formula for the mean of a discrete random variable is,
The mean of the random variable is obtained as given below:
x | P(x) | |
0 | 0.10 | 0.0 |
1 | 0.25 | 0.3 |
2 | 0.30 | 0.6 |
3 | 0.20 | 0.6 |
4 | 0.10 | 0.4 |
5 | 0.05 | 0.3 |
Total | 1.00 | 2.1 |
Thus, the mean value is 2.10.
f.
Find the standard deviation.
f.
Answer to Problem 42E
The standard deviation is 1.30.
Explanation of Solution
Calculation:
The standard deviation of the random variable X is obtained by taking the square root of variance.
The formula for the variance of the discrete random variable X is,
Where
The variance of the random variable X is obtained using the following table:
x | P(x) | |||
0 | 0.10 | –2.1 | 4.41 | 0.44 |
1 | 0.25 | –1.1 | 1.21 | 0.30 |
2 | 0.30 | –0.1 | 0.01 | 0.00 |
3 | 0.20 | 0.9 | 0.81 | 0.16 |
4 | 0.10 | 1.9 | 3.61 | 0.36 |
5 | 0.05 | 2.9 | 8.41 | 0.42 |
Total | 2.4 | 18.46 | 1.69 |
Therefore,
Thus, the variance is 1.69.
The standard deviation is,
That is, the standard deviation is 1.30.
g.
Find the probability that it will take more than 6 minutes for all the customers currently in line to checkout.
g.
Answer to Problem 42E
The probability that it will take more than 6 minutes for all the customers currently in line to checkout is 0.35.
Explanation of Solution
Calculation:
Each customer will take three minutes to check out. If the number of customers is 1 then it will take 3 minutes, if the number of customers is 2 it will take 6 minutes, if the number of customers is 3 or more then it will take more than 6 minutes.
Thus, the probability that that it will take more than 6 minutes for all the customers currently in line to checkout is the sum of the probabilities at
Substituting the values from the probability distribution table,
Thus, the probability that it will take more than 6 minutes for all the customers currently in line to checkout is 0.35.
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Chapter 5 Solutions
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