Question

When jai commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 39 minutes and a standard deviation of 4.5 minutes. using the empirical rule, determine the interval that represents the middle 95% of his commute times.

Answer 1

The middle 95% of Jai's commute times, according to the empirical rule, is between 30 to 48 minutes.

Step-by-step explanation:

Using the empirical rule (also known as the 68-95-99.7 rule), we can determine that for a normal distribution with a mean (μ) of 39 minutes and a standard deviation (σ) of 4.5 minutes, the middle 95% of Jai's commute times fall within 2 standard deviations of the mean. This interval is found by subtracting and adding 2 standard deviations to the mean. To calculate this interval, we perform the following steps:

• Calculate the lower bound: 39 - (2 × 4.5) = 39 - 9 = 30 minutes.
• Calculate the upper bound: 39 + (2 × 4.5) = 39 + 9 = 48 minutes.

Therefore, the interval that represents the middle 95% of Jai's commute times is 30 to 48 minutes.