Simplify 7 - (-4) + 3(-6)
2 answers:
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Answer:
(a) The relative frequency of people who take between 49 and 65 minutes to complete the test is 0.6826.
(b) The middle 95% of completion times for all people taking the test is in the interval (41, 73).
Step-by-step explanation:
Let <em>X</em> = length of time required complete a certain test.
It is provided that <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 57 minutes and standard deviation, <em>σ</em> = 8 minutes.
(a)
Compute the probability of people who take between 49 and 65 minutes to complete the test as follows:
*Use the <em>z</em>-table for the probability.
Thus, the relative frequency of people who take between 49 and 65 minutes to complete the test is 0.6826.
The graph is provided below.
(b)
According to the Empirical rule, for a normal distribution:
- 68% of the observation fall within 1 standard deviation of mean.
- 95% of the observation fall within 2 standard deviation of mean.
- 99.7% of the observation fall within 3 standard deviation of mean.
Then, P (μ - 2σ < X < μ + 2σ) = 0.95
Compute the limits as follows:
Thus, the middle 95% of completion times for all people taking the test is in the interval (41, 73).
