Question

the average sale price (online) for a certain brand of professional mountain bike is approximately normally distributed with a mean of $4200 and a standard deviation of $250. find the 31st percentile of this distribution. (round to 2 decimal places.)

Explanation:

Step1: Find the z - score for 30th percentile

We look up the z - score in the standard normal distribution table (z - table) for an area of 0.30. The z - score corresponding to an area of 0.30 is approximately $z=- 0.52$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the original distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to solve for $x$. Rearranging the formula gives $x=\mu + z\sigma$.
We know that $\mu = 4200$ and $\sigma=250$ and $z=-0.52$.
Substitute the values into the formula: $x = 4200+(-0.52)\times250$.

Step3: Calculate the value of x

First, calculate $(-0.52)\times250=-130$. Then, $x = 4200 - 130=4070.00$.

Answer:

$4070.00$