STATS
Last 4 ID____________________
Quiz on Z-scores given percentiles
Period______
1.
What z-score corresponds with the area above?
invNorm(0.1635,0,1)=-0.98017
2. What z-score corresponds with the graph below?
0.5000+0.2257=0.7257
invNorm(0.7257,0,1)=0.599859
3. What z-score is a percentile of 75%?
invNorm(0.75,0,1)=0.6744897
4. What z-score is a percentile of 25%?
invNorm(0.25,0,1)=-0.6744897
For 2015 college bound students, the SAT math scores had a mean of 511 with a standard deviation of 120.
5. What score would you have to get to be in the 90th percentile of all students?
invNorm(0.9,511,120)=664.786, so about 665
6. What score would you have to get to be better than 50% of all students?
511, the mean represents the 50th percentile, which is better than 50% of all students
7. Mike is in the 99th percentile for his height. U.S. men have an average height of 69.3 inches
with a standard deviation of 2.8 inches. How tall is he?
invNorm(0.99,69.3,2.8)=75.81377, so about 76 inches or 6’4”
8. In a field, the heights of sunflowers are normally distributed with a mean of 72 inches and
standard deviation of 4 inches. Find the corresponding percentile for a sunflower that is 1.6 standard
deviations greater than the mean.
normalcdf(-10,1.6,0,1)=0.945, so about 95th
9. The weights of ripe watermelons grown at Mr. Smith’s farm are normally distributed with a
standard deviation of 2.8 lb. Find the mean weight of Mr. Smith’s ripe watermelons if only
3% weigh less than 15 lb.
𝛔 = 𝟐. 𝟖
𝐱 = 𝟏𝟓
invNorm(0.03,0,1)=-1.88z-score
𝐱−𝛍
𝐳=
𝛔
𝟏𝟓 − 𝛍
−𝟏. 𝟖𝟖 =
𝟐. 𝟖
20.264=𝛍, so about 20lb