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More Stats Practice:
1. Without the TI-83, determine the mean, median, mode, and standard deviation for the data shown
on a set of classmarks, draw a histogram with a bin width of 10 for the data:
2.
68, 56, 45, 32, 89, 65, 75, 74, 75, 82, 87, 98, 70, 66, 45, 72, 55, 75, 80, 90
3. A large sample yields a bell-shaped histogram with a mean ( x ) and a standard deviation ( S x ).
Approximately what percentage of the sample would lie in the intervals with the limits shown ?
a. x to x  3S x
b x  S x to x  2S x
4. Use the 68-95-99.7 rule on a distribution of values with a population mean of 150 and a
population standard deviation of 15 to answer the following questions. What percentage of the
data would measure :
a. Between 105 and 165.
b. Between 120 and 150.
5. A sample of 200 bolts used in a certain automobile has a mean of 140 grams and a standard
deviation of 1.7 grams.
a. If the distribution of the bolt masses is bell shaped, approximately how many bolts are
within 3.4 grams of the mean.
b. How many bolts are between 138.3 grams and 143.4 grams
6. A sample of 750 tires has a mean lifespan of 45000 km and a standard deviation of 2000 km.
a. If the distribution of tire lifespan is bell shaped, approximately how many tires are within
4000 km of the mean?
b. What range of tire lifespan would consist of 68 % of the data.
7. Two different normal distribution curves representing different populations follow.
a. Which population has the largest population mean? Explain why.
b. Which population has the largest population standard deviation? Explain why.
c. Which would contain a larger sample of data? Explain.
10
y
9
8
7
6
5
4
3
2
1
x
5
10
15
ANSWERS:
Worksheet on Normal Distribution
1. (a) 28000 and 32000
(b) 26000 & 34000
2. (a) 68 %
(b) 34%
(c) 2.5%
3. (a) 2.5%
(b) 320
(c) 97.5%
(d) 16%
4. yes – more than 2 standard deviations away from the mean.
5. (a) 6800
(b) 500
6. (a) 2.5%
(b) 200
7. 1250
8. (a) 2.5%
(b) 16%
9. (a) 475
(b) 840
10. (a) 800
(b) 125
(c) 81.5%
(d) 97.5%
More Stats Practice:
1. mean = 69.95
median = 73
Standard deviation = 16.75 (sample)
Bin
30-40
40-50
50-60
60-70
70-80
80-90
90-100
10
9
8
7
6
5
4
3
2
1
0
mode = 75
Freq
1
2
2
3
6
4
2
Frequency
Bin
20
30
40
50
60
70
80
90
100
(d) 1680
2. (a) 49.85%
(b) 81.5%
3. (a) 83.85%
(b) 47.5%
4, (a) 95%
(b) 163 bolts
5, (a) 713
(b) 43000 to 47000
6. (a) 2nd – the mean is farther to the right on the x scale
(b) first – more spread out
(c) 2nd – higher frequency numbers