Question

Suppose your statistics professor reports test grades as​ z-scores, and you got a score of 2.492.49 on an exam. ​a) Write a sentence explaining what that means. ​b) Your friend got a​ z-score of negative 2−2. If the grades satisfy the Nearly Normal​ Condition, about what percent of the class scored lower than your​ friend? ​a) Choose the correct answer below. A. The score was 2.492.49 points higher than the mean score in the class. B. The score was 2.492.49 points lower than the mean score in the class. C. The score was 2.492.49 standard deviations higher than the mean score in the class. D. The score was 2.492.49 standard deviations lower than the mean score in the class.

Answer 1

Answer:

a) Option C) The score was 2.49 standard deviations higher than the mean score in the class.

b) 2.3%

Step-by-step explanation:

a) We are given that the distribution of test grades is a bell shaped distribution that is a normal distribution.

Formula:

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

$\displaystyle\frac{x-\mu}{\sigma} = 2.49\\\\x - \mu = 2.49\sigma\\x = \mu + 2.49\sigma$

Option C) The score was 2.49 standard deviations higher than the mean score in the class.

b) The z-score for a particular score is -2.

We have to evaluate

P(z < -2)

Calculating the value from normal z-table.

$P(z < -2) = 0.023$

Thus, 2.3% of  of the class scored lower than my​ friend.