Question

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. Below what value are approximately 97.5% of the students?
a. $215
b. $195
c. $255
d. $275
e. $295

Answer 1

Answer:

Option D) $275

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $235

Standard Deviation, σ = $20

We are given that the distribution of amount of money spent by students is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.975

$P( X < x) = P( z < \displaystyle\frac{x - 235}{20})=0.975$  

Calculation the value from standard normal z table, we have,  

$P( z < 1.960) = 0.975$

$\displaystyle\frac{x - 235}{20} = 1.960\\x =274.2 \approx 275$

Approximately 97.5% of the students spent below $275 on textbook.