Question

question
when harper commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 20 minutes and a standard deviation of 3.5 minutes. what percentage of her commutes will be shorter than 23 minutes, to the nearest tenth?

Explanation:

Step1: Calculate the z-score

The z-score formula is $z=\frac{x-\mu}{\sigma}$, where $x=23$, $\mu=20$, $\sigma=3.5$.
$z=\frac{23-20}{3.5}=\frac{3}{3.5}\approx0.8571$

Step2: Find cumulative probability

Use a z-table or calculator to find $P(Z<0.8571)$. This value is approximately 0.8043.

Step3: Convert to percentage

Multiply the probability by 100 and round to the nearest tenth.
$0.8043\times100=80.43\approx80.4$

Answer:

80.4%