Question

1. the distribution of ticket prices for concerts in a large city is approximately normal, with a mean of $112 and a standard deviation of standard deviation of $25. tami believes the percentage of tickets that cost between $100 and $120 is larger than the percentage of tickets that cost between $120 and $140. marcia believes the percentage of tickets that cost between $100 and $120 is smaller than the percentage of tickets that cost between $120 and $140. eugene believes the percentage of tickets that cost between $100 and $120 is the same as the percentage of tickets that cost between $120 and $140. who is correct?

a. tami
b. marcia
c. eugene
d. tami, marcia, and eugene are all incorrect.
e. this question cannot be answered without more information.

Explanation:

Step1: Calculate z - scores for $100 and $120

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 112$ and $\sigma=25$.
For $x = 100$, $z_1=\frac{100 - 112}{25}=\frac{- 12}{25}=-0.48$.
For $x = 120$, $z_2=\frac{120 - 112}{25}=\frac{8}{25}=0.32$.
The percentage of tickets between $100 and $120 is $P(-0.48

Step2: Calculate z - scores for $120 and $140

For $x = 120$, $z_2 = 0.32$ (calculated above).
For $x = 140$, $z_3=\frac{140 - 112}{25}=\frac{28}{25}=1.12$.
The percentage of tickets between $120 and $140 is $P(0.32

Step3: Compare the two probabilities

We know that the standard normal distribution is symmetric about $z = 0$.
The area between $z=-0.48$ and $z = 0.32$ is larger than the area between $z = 0.32$ and $z = 1.12$ because the tails of the normal distribution get thinner as we move away from the mean.
So, the percentage of tickets that cost between $100 and $120 is larger than the percentage of tickets that cost between $120 and $140. Tami is correct.

Answer:

A. Tami