Z-score and percentile
. answer with explanation. both circled numbers

I assume all these measures are normally distributed, in which case the median and mean are equal.

15a. because the normal distribution is symmetric about the mean, and so 50% of families have an income greater than the average.

15b. by definition of percentile. The 90th percentile is $178,500, so the top 10% of families earn more than this.

15c. Because it's continuous, this distribution has the property . The top 10% earn more than $178,500, so the remaining 90% earn less. 50% of families earn more than the average, so 50% of families earn less than the average. Then so 40% of families earn between the median and 90th percentile.

16a. or 75% because the first quartile is $570, meaning 25% of renters pay less than this amount.

16b. or 50% by the same reasoning used in (15a).

16c. or 25% by the same reasoning as in (15c).