When Serenity commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 39 minutes and a standard deviation of 5 minutes Using the empirical rule, determine the interval that represents the middle 99.7% of her commute times.
Answers
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case
Step-by-step explanation:
For this case we can define the random variable X as the amount of time it takes her to arrive to work and we know that the distribution for X is given by:
And we want to use the empirical rule to estimate the middle 95% of her commute times. And the empirical rule states that we have 68% of the values within one deviation from the mean, 95% of the values within two deviations from the mean and 99.7 % of the values within 3 deviations from the mean. And we can find the limits on this way:
So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case
Answer: (24,54)
Step-by-step explanation:
99.7% of commutes fall between 24 and 54