when brooklyn commutes to work, the amount of time it takes her to arrive is normally distributed with a…

when brooklyn commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of her commutes will be between 40 and 50 minutes?

when brooklyn commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of her commutes will be between 40 and 50 minutes?

Answer

Answer:

68%

Explanation:

Step1: Identify the intervals

The mean is $\mu = 45$ minutes and the standard - deviation is $\sigma=5$ minutes. The lower bound $40 = 45 - 5=\mu-\sigma$ and the upper bound $50 = 45 + 5=\mu+\sigma$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 68% of the data lies within 1 standard - deviation of the mean, i.e., in the interval $(\mu - \sigma,\mu+\sigma)$. So the percentage of her commutes between 40 and 50 minutes is 68%.