Percentiles & Z-Scores
Transforming Data
Density Curves & Empirical Rule
Using Table A: Areas & Z-Scores
Just for Fun
100
A student is at the 80th percentile on a test. What does that mean?
She scored higher than about 80% of the students (NOT 80% of the questions right)
100
Adding 5 points to every score changes the mean by this much.
The mean increases by 5
100
The total area under this density curve equals this number.
1
100
Use Table A. Find the area to the left of z = 1.25.
0.8944 (about the 89th percentile)
100
This city is the capital of Florida.
Tallahassee
200
Use the graph of test scores. What percentile is a score of 80?
The 60th percentile
200
Every student gets +5 curve points. What happens to the standard deviation?
It stays the same
200
This is the shape of every normal curve.
Symmetric, single-peaked, and bell-shaped
200
Use Table A. The area to the left of z is 0.9750. What is z?
z = 1.96
200
An octopus has this many hearts.
3
300
A test has mean 72 and SD 8. Find the z-score for a score of 84.
z = 1.5, because (84 - 72) / 8 = 1.5
300
Heights have mean 66 in. and SD 3 in. After multiplying by 2.54 to convert to cm, find the new mean and SD.
Mean = 167.64 cm, SD = 7.62 cm
300
The shaded region is within 2 standard deviations of the mean. About what percent of the data is in it?
About 95%
300
Use Table A. What proportion of a normal distribution lies above z = 1.50?
0.0668, because 1 - 0.9332 = 0.0668
300
This is the only letter of the alphabet that doesn't appear in the name of any U.S. state.
Q
400
Ava scored 85 on a test (mean 70, SD 10). Ben scored 30 on a different test (mean 22, SD 4). Who did better compared to his or her own class?
Ben. His z = 2, and Ava's z = 1.5.
400
The boxplot shows waiting times in minutes. Every time is changed using new = 2(old) + 5. Find the new median and IQR.
Median = 55, IQR = 30 (old median 25, old IQR 35 - 20 = 15)
400
Battery life is approximately normal with mean 400 hours and SD 30. About what percent of batteries last more than 460 hours (shaded)?
About 2.5% (460 is 2 SDs above the mean)
400
Quiz times are approximately normal with mean 20 min and SD 4 min. The fastest 10% earn a prize. What is the cutoff time?
About 14.88 minutes (z = -1.28, and 20 + (-1.28)(4) = 14.88)
400
An adult human body has this many bones
206
500
A quiz has mean 80 and SD 6. Kayla's z-score is -0.5. What score did she earn?
77, because 80 + (-0.5)(6) = 77
500
Scores are changed with new = 0.5(old) + 50. The old data had mean 60, SD 12, and IQR 16. Find the new mean, SD, and IQR.
Mean = 80, SD = 6, IQR = 8
500
A data set of n = 200 has mean 50 and SD 10 and is approximately normal. About how many values fall between 40 and 70 (shaded)?
About 163 values (34% + 47.5% = 81.5%, and 0.815 x 200 = 163)
500
Quiz times are approximately normal with mean 20 min and SD 4 min. What proportion finish between 16 and 22 minutes (shaded)?
0.5328 (z = -1.00 gives 0.1587, z = 0.50 gives 0.6915, and 0.6915 - 0.1587 = 0.5328)
500
This is the only mammal capable of true, sustained flight.
The bat