The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean = 100 and standard deviation = 15.

Approximately what percent of the scores fall in the range from 75 and 100?

A score in what range would represent the top 16% of the scores?

Question

The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean = 100 and standard deviation = 15. 

Approximately what percent of the scores fall in the range from 75 and 100?

A score in what range would represent the top 16% of the scores?

kropot72 · Answer

Do you know how to work out the z-score for 75? It is done as follows:
$$z=\frac{X-\mu}{\sigma}=\frac{75-100}{15}=you\  can\  calculate$$
The z-score for 100 is 0.
Using the z-scores you need to refer to a standard normal distribution table and then calculate the required percentage.

kropot72 · Answer

@cynthia123 Can you follow the explanation?

anonymous · Answer

yes, @kropot72 thank you ! 
so to find the percentile of the zscore 0 how would i do that ?

kropot72 · Answer

Reference to a standard normal distribution table shows that the cumulative probabilities for z-scores of 0 and -1.667 are 0.500 and 0.048 respectively. therefore the percentage of scores that fall in the range from 75 to 100 are given by
$$(0.500-0.048)\times 100=\ ?\ percent$$