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WorksheetsNormal Distributions and Empirical Rule AMDM
Total questions: 45
Worksheet time: 2hrs 17mins
Name
Class
Date
1.
By the way, what is standard deviation?
a)
good question
b)
how standardly something deviates
c)
average distance that data points are from the average
d)
Idk but I should probably find out pretty soon
2.
This data is normally distributed. What percent of the data is in the shaded region?
a)
68%
b)
95%
c)
99.7%
d)
50%
3.
This data is normally distributed. What percent of the data is in the shaded region?
a)
68%
b)
95%
c)
99.7%
d)
50%
4.
This data is normally distributed. What percent of the data is in the shaded region?
a)
68%
b)
95%
c)
99.7%
d)
50%
5.
This data is normally distributed. What percent of the data is in the shaded region?
a)
68%
b)
32%
c)
95%
d)
50%
6.
The data is normally distributed. What percentage of the data is in the shaded region?
a)
68%
b)
34%
c)
50%
d)
84%
7.
Which curve has the greater standard deviation?
a)
Red
b)
Black
c)
Blue
8.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.
About what percent of the products last 6 days or less?
About what percent of the products last 6 days or less?
a)
68%
b)
34%
c)
16%
d)
2.5%
9.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.
About what percent of the products last between 12 and 15 days?
About what percent of the products last between 12 and 15 days?
a)
68%
b)
34%
c)
16%
d)
2.5%
10.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
11.
If the shaded area under the curve is .85, what is the other missing portion of the curve?
a)
.26
b)
.15
c)
.30
d)
.17
12.
The normal curve is symmetrical about the mean.
a)
True
b)
False
13.
Find x ≥ x̄ + 1σ
a)
97.5
b)
13.5
c)
84
d)
16
14.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
15.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the GPA of the highest 2.5% of the students?
a)
4.1
b)
4.1 or higher
c)
4.7
d)
4.5 or higher
16.
Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? Calculate the probability.
a)
2.5%
b)
2.35%
c)
16%
d)
13.5%
17.
In a population, if μ=125 and σ=25, how common are values in the 100 – 175 range?
a)
68%
b)
84%
c)
81.5%
d)
95%
18.
The mean life of a tire is 30,000 km. The standard deviation is 2000 km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
a)
28,000 km and 32,000 km.
b)
24,000 km and 34,000 km.
c)
26,000 km and 34,000 km.
d)
27,000 km and 31,000 km.
19.
Between what two standard deviations of a normal distribution contain 68% of the data?
a)
one below and one above
b)
two below and two above
c)
two below and zero
d)
zero and two above
20.
The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?
a)
92.4%
b)
10.5%
c)
16%
d)
7.6%
21.
Pat and Chris both took a spatial abilities test (mean = 80, std. dev. = 8). Pat scores a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris?
a)
26.8%
b)
96%
c)
65.1%
d)
4%
22.
The weights of adult male beagles are normally distributed, with a mean of 25 pounds and a standard deviation of 3 pounds. A beagle is randomly selected. Find the probability that the beagle’s weight is more than 28 pounds.
a)
0.84
b)
0.34
c)
0.16
d)
0.50
23.
1. The average age of a group of fans at a hockey game is 36 years with a standard deviation of 8 years. What percent of fans are between 20 and 28 years old?
a)
34%
b)
16%
c)
13.5%
d)
2.5%
24.
What does the Mean tell you about a data set?
a)
It tells you the average of the data set
b)
It tells you the number that is used the most
c)
It tells you the difference between the highest and lowest number
d)
It tells you the mood of the data set
25.
The number of pages that Carolyn wrote in her journal each day from Monday to Friday is shown below:
9, 8, 12, 6, 10
What is the mean number of pages she wrote per day?
9, 8, 12, 6, 10
What is the mean number of pages she wrote per day?
a)
5
b)
6
c)
9
d)
11
26.
Find the range.
5, 15, 10, 20, 15, 10, 15
(highest value minus lowest)
5, 15, 10, 20, 15, 10, 15
(highest value minus lowest)
a)
5
b)
10
c)
15
d)
13
27.
At Dominique's Donuts the number of donut holes in a bag can vary. Help Dominique find the mode.
12,10,10,10,13,12,11,13,10
12,10,10,10,13,12,11,13,10
a)
13
b)
12
c)
11
d)
10
28.
Ervin bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Ervin's scores?
a)
193
b)
127
c)
60
d)
66
29.
What is the mode?
a)
# happening the most
b)
the average
c)
biggest - smallest
d)
the middle #
30.
Find the mean of these numbers:
5,11,2,12,4,2
5,11,2,12,4,2
a)
4.1
b)
6
c)
4.5
d)
4
31.
Find the median, mode and range:
3, 5, 7, 9, 11, 8, 3
3, 5, 7, 9, 11, 8, 3
a)
median:7 mode:3 range:7
b)
median:6 mode:3 range:7
c)
median:7 mode:3 range:8
32.
To find the mean of a set of numbers, add up all the items and divide by...
a)
2
b)
The minimum
c)
The maximum
d)
The number of items
33.
What is the range?
a)
average
b)
biggest-smallest
c)
the middle #
d)
# happening the most
34.
A data set can have more than one mode
a)
True
b)
False
35.
The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. Approximately what percent of days in February will have days below 23 degrees?
a)
5%
b)
34%
c)
50%
d)
68%
36.
1. Which best describes the shaded part of this normal distribution graph?
a)
All data that is one or higher.
b)
All data that is one or more standard deviations above the mean.
c)
All data that is between 1 and 3.
d)
All data that is above the mean.
37.
68% of fireman worked between what years?
a)
Between 5 and 15 years
b)
Between 10 and 30 Years
c)
Between 15 and 25 years
d)
Between 17 and 23 years
38.
What is the Normal Range (68%) of the monthly salary of teachers if the average is $4,000.00 with a standard deviation of 3,000?
a)
1000-7000
b)
3000-4000
c)
1000-4000
d)
4000-7000
39.
A machine produces electrical components.
99.7% of the components have lengths between 1.176 cm and 1.224 cm.
Assuming this data is normally distributed, what are the mean and standard deviation?
99.7% of the components have lengths between 1.176 cm and 1.224 cm.
Assuming this data is normally distributed, what are the mean and standard deviation?
a)
Mean = 1.210 cm
S.D. = 0.008 cm
S.D. = 0.008 cm
b)
Mean = 1.200 cm
S.D. = 0.004 cm
S.D. = 0.004 cm
c)
Mean = 1.190 cm
S.D. = 0.008 cm
S.D. = 0.008 cm
d)
Mean = 1.200 cm
S.D. = 0.008 cm
S.D. = 0.008 cm
40.
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?
a)
1084 to 1216 pounds
b)
1106 to 1150 pounds
c)
1106 to 1194 pounds
d)
1128 to 1172 pounds
41.
A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.
a)
2.5%
b)
.15%
c)
2.35%
d)
2.25%
42.
Students pass a test if they score 50% or more.
The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.
Assuming this data is normally distributed, what percentage of students pass the test?
The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.
Assuming this data is normally distributed, what percentage of students pass the test?
a)
5
b)
16
c)
24
d)
32
43.
Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3?
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
44.
Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3?
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
45.
Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3?
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
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