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 mean and standard deviation

Mean ($\mu$) = 45, Standard Deviation ($\sigma$) = 5.

Step2: Find how many standard deviations from mean

For 35: $ \frac{35 - 45}{5} = -2 $ (2 standard deviations below mean).
For 55: $ \frac{55 - 45}{5} = 2 $ (2 standard deviations above mean).

Step3: Apply empirical rule

Empirical rule states that for normal distribution, about 95% of data lies within 2 standard deviations of mean.

Answer:

95%