Question

In Drew's town the average price for a tutor is $15 per hour, and the standard deviation is $5.25 per hour. In Drew's town, what is the probability that a tutor charges between $10 and $20 per hour? Assume that tutoring prices are normally distributed.

Answer 1

0.659 is the probability that a tutor charges between $10 and $20 per hour.

Explanation:

We are given the following information in the question:

Mean, μ = $15 per hour

Standard Deviation, σ = $5.25 per hour

We are given that the distribution of tutoring prices is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P( tutor charges between $10 and $20 per hour)

`P(10 \leq x \leq 20)\\\\ = P(\displaystyle(10 - 15)/(5.25) \leq z \leq \displaystyle(20-15)/(5.25))\\\\ = P(-0.9523 \leq z \leq 0.9523)\\\\= P(z \leq 0.9523) - P(z < -−0.9523)\\= 0.8295 - 0.1705= 0.659`

0.659 is the probability that a tutor charges between $10 and $20 per hour.