Concept explainers
a.
Find the value of
a.
Answer to Problem 46E
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 46E
The probability value,
Explanation of Solution
Calculation:
The required probability can be obtained as shown below:
Substituting the value from the probability distribution table,
Thus, the probability value,
c.
Find the probability that three or more of the teenagers sent text messages.
c.
Answer to Problem 46E
The probability that three or more of the teenagers sent text messages is 0.63.
Explanation of Solution
Calculation:
The probability that three or more of the teenagers sent text messages is the sum of the probabilities at
Substituting the values from the probability distribution table,
Thus, the probability that three or more of the teenagers sent text messages is 0.63.
d.
Find the probability that fewer than two of the teenagers sent text messages.
d.
Answer to Problem 46E
The probability that fewer than two of the teenagers sent text messages is 0.112.
Explanation of Solution
Calculation:
The probability that fewer than two of the teenagers sent text messages is the sum of the probabilities at
Substituting the values from the probability distribution table,
Thus, the probability that fewer than two of the teenagers sent text messages is 0.112.
e.
Find the
e.
Answer to Problem 46E
The mean value is 2.85.
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 | 0.015 | 0.000 |
1 | 0.097 | 0.097 |
2 | 0.258 | 0.516 |
3 | 0.343 | 1.029 |
4 | 0.227 | 0.908 |
5 | 0.060 | 0.300 |
Total | 1.000 | 2.850 |
Thus, the mean value is 2.85.
f.
Find the standard deviation.
f.
Answer to Problem 46E
The standard deviation is 1.107.
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 | ||||
0 | 0.015 | –2.85 | 8.1225 | 0.122 |
1 | 0.097 | –1.85 | 3.4225 | 0.332 |
2 | 0.258 | –0.85 | 0.7225 | 0.186 |
3 | 0.343 | 0.15 | 0.0225 | 0.008 |
4 | 0.227 | 1.15 | 1.3225 | 0.300 |
5 | 0.060 | 2.15 | 4.6225 | 0.277 |
Total | 1.000 | –2.1 | 18.235 | 1.226 |
Therefore,
Thus, the variance is 1.226.
The standard deviation is,
That is, the standard deviation is 1.107.
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Chapter 5 Solutions
Essential Statistics
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