Question

when eva commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 57 minutes and a standard deviation of 4 minutes. using the empirical rule, determine the interval that represents the middle 95% of her commute times. answer attempt 1 out of 2

Explanation:

Step1: Recall the empirical rule

The empirical rule states that for a normal distribution, about 95% of the data lies within \( \mu\pm2\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Calculate the lower bound

The lower bound is \(\mu - 2\sigma\). Given \(\mu = 57\) and \(\sigma=4\), we have \(57-2\times4=57 - 8 = 49\).

Step3: Calculate the upper bound

The upper bound is \(\mu + 2\sigma\). So \(57+2\times4=57 + 8=65\).

Answer:

The interval that represents the middle 95% of her commute times is \(49\) minutes to \(65\) minutes.