Question

normal distribution - empirical rule
question
when abdoulaye commutes to work, the amount of time it takes him 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 his commutes will be between 35 and 55 minutes?

Explanation:

Step1: Identify the mean and standard deviation

The mean ($\mu$) is 45 minutes and the standard deviation ($\sigma$) is 5 minutes.

Step2: Find how many standard deviations 35 and 55 are from the mean

For 35: $45 - 35 = 10$, and $10\div5 = 2$ standard deviations below the mean.
For 55: $55 - 45 = 10$, and $10\div5 = 2$ standard deviations above the mean.

Step3: Apply the empirical rule

The empirical rule states that for a normal distribution, about 95% of the data lies within 2 standard deviations of the mean.

Answer:

95%