Question

the average sale price (online) for a certain brand of professional mountain bike is approximately normally distributed with a mean of $4,200 and a standard deviation of $250. find the 30th percentile of this distribution. (round to 2 decimal places.)

Explanation:

Step1: Find the z - score for the 30th percentile

We use the standard normal distribution table (z - table). The z - score corresponding to a cumulative probability 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 we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know that $\mu = 4200$, $\sigma=250$, and $z=-0.52$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate the value of $x$

Substitute the values into the formula: $x = 4200+(-0.52)\times250=4200 - 130=4070.00$.

Answer:

$4070.00$