Question

Use technology or a z-score table to answer the question. Scores on a standardized exam are normally distributed with a mean of 59 and a standard deviation of 8. Consider a group of 5000 students. Approximately how many students will score less than 67 on the exam?

Answer 1

Answer:

Approximately 4200 students will score less than 67 on the exam.

Step-by-step explanation:

Given:

Scores are normally distributed.

Mean score is, $\mu=59$

Standard deviation is, $\sigma=8$

Score is, $x=67$

Total number of students, $n=5000$

Now, the z score is given as:

$z=\frac{x-\mu}{\sigma}\\\\z=\frac{67-59}{8}=\frac{8}{8}=1$

Since, the score is less than 67, therefore, z-score must be less than 1. So,

$z$

From the z-score table, we observe that for z < 1, the population is 0.8413 or 84.13 % of the total population.

Therefore, the number of students scoring less than 67 is given as:

$Number\ less\ than\ 67\ score=0.8413\times 5000=4206.7\approx 4200$

So, approximately 4200 students out of 5000 will get a score less than 67.