Question

Z-score and Percentile Help please. Answer with explanation. Both circled numbers

Answer 1

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

15a. $P(X>66,650)=0.5$ because the normal distribution is symmetric about the mean, and so 50% of families have an income greater than the average.

15b. $P(X>178,500)=0.1$ 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 $P(66,650$. 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 $P(66,650$ so 40% of families earn between the median and 90th percentile.

16a. $P(X>570)=0.75$ or 75% because the first quartile is $570, meaning 25% of renters pay less than this amount.

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

16c. $P(570$ or 25% by the same reasoning as in (15c).