Concept explainers
a.
To Construct the probability distribution of the given data.
a.
Explanation of Solution
Given:
Number of Tests | Frequency (in 1000s) |
1 | 953 |
2 | 423 |
3 | 194 |
4 | 80 |
5 | 29 |
6 | 9 |
7 | 3 |
8 | 1 |
Total | 1692 |
To get the probability distribution of no. of tests taken, it is required to divide the respective frequency of no. of test taken by the total frequency.
The probability distribution is given below:
Number of Tests | Frequency (in 1000s) | P (X = x) |
1 | 953 | 0.563 |
2 | 423 | 0.250 |
3 | 194 | 0.115 |
4 | 80 | 0.047 |
5 | 29 | 0.017 |
6 | 9 | 0.005 |
7 | 3 | 0.002 |
8 | 1 | 0.001 |
Total | 1692 | 1.000 |
b.
To find the probability that student took only one exam.
b.
Answer to Problem 4RE
Probability that student took only one exam = 0.563
Explanation of Solution
Calculation:
To get the probability distribution of no. of tests taken, it is required to divide the respective frequency of no. of test taken by the total frequency.
The probability distribution is given below:
Number of Tests | Frequency (in 1000s) | P (X = x) |
1 | 953 | 0.563 |
2 | 423 | 0.250 |
3 | 194 | 0.115 |
4 | 80 | 0.047 |
5 | 29 | 0.017 |
6 | 9 | 0.005 |
7 | 3 | 0.002 |
8 | 1 | 0.001 |
Total | 1692 | 1.000 |
Calculation:
c.
To find the mean
c.
Answer to Problem 4RE
The mean of the given distribution is 1.73.
Explanation of Solution
Formula Used:
Calculation:
Number of Tests | Frequency (in 1000s) | P (X = x) | |
1 | 953 | 0.563 | 0.56 |
2 | 423 | 0.250 | 0.50 |
3 | 194 | 0.115 | 0.34 |
4 | 80 | 0.047 | 0.19 |
5 | 29 | 0.017 | 0.09 |
6 | 9 | 0.005 | 0.03 |
7 | 3 | 0.002 | 0.01 |
8 | 1 | 0.001 | 0.00 |
Total | 1692 | 1.000 | 1.73 |
The mean
d.
To find the mean
d.
Answer to Problem 4RE
Standard Deviation = 1.05
Explanation of Solution
Formula Used:
Calculation:
Number of Tests | Frequency (in 1000s) | P (X = x) | ||
1 | 953 | 0.563 | 0.56 | 0.56 |
2 | 423 | 0.250 | 0.50 | 1.00 |
3 | 194 | 0.115 | 0.34 | 1.03 |
4 | 80 | 0.047 | 0.19 | 0.76 |
5 | 29 | 0.017 | 0.09 | 0.43 |
6 | 9 | 0.005 | 0.03 | 0.19 |
7 | 3 | 0.002 | 0.01 | 0.09 |
8 | 1 | 0.001 | 0.00 | 0.04 |
Total | 1692 | 1.000 | 1.73 | 4.10 |
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Chapter 6 Solutions
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