Deck 6: The Normal Distribution

Question 1

The following formula can be used to find a specific value in a normal population:

Answer 1

True

Question 2

The area under the curve is always positive even if the z value is negative.

Answer 2

True

Question 3

The z value corresponding to 48.81% of the data is 2.20 in Table E of Appendix

Answer 3

False

Question 4

The figure below is an example of a negatively skewed distribution.

Question 5

A random sample of size 4 is selected from population A which has a standard deviation of 6 and a
random sample of size 16 is selected from population B which has a standard deviation of 10.The
standard error of the mean for the sample from population A is smaller than that for the sample from
population

Question 6

Which of the following properties does not apply to a theoretical normal distribution?

A)The normal distribution is bell-shaped.
B)The mean, median, and mode are equal.
C)The normal distribution is bimodal.
D)The curve never touches the x-axis.

Question 7

The area under the normal distribution curve that lies within three standard deviations of the mean is
approximately 95%.

Question 8

On an easy test, the mean score was 97 out of a possible 100 points.The distribution of all test scores is mostly likely to be

A)symmetric
B)negatively skewed
C)positively skewed
D)diagonally skewed

Question 9

The z value that corresponds to the percentile is z = 1.72.

Question 10

The total area under the normal distribution curve is approximately 0.99 but can never be equal to 1.0.

Question 11

In applied statistics, the area under the normal distribution curve is more important than the
frequencies.

Question 12

The standard deviation of sample means will be larger than the standard deviation of the population, and
it will be equal to the population standard deviation multiplied by the square root of the sample size.

Question 13

The is 0.4878.

Question 14

Give the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean?

A)symmetrical
B)positively skewed
C)negatively skewed
D)left skewed

Question 15

If one wishes to compute the probability that the mean of sample selected from a normal population is
less than a particular value, one should correct for continuity if the sample size is less than 30.

Question 16

The normal distribution curve can be used as a probability distribution curve for normally distributed
variables.

Question 17

The area under the normal distribution curve that lies within three standard deviations of the mean is
approximately 95%.

Question 18

When the majority of the data values fall to the right of the mean, the distribution is said to be left
skewed.

Question 19

The area to the right z = 1.83 of is 0.4256.

Question 20

When finding the area under the curve between two z values, the procedure is to subtract the two z values
and look up the corresponding area in Table E of Appendix

Question 21

For a normal curve with mean 5 and standard deviation 7, which of the following parts of the normal curve will have an area of approximately 68%?

A)from 1.5 to 8.5
B)from -2 to 12
C)from 5 to 19
D)from -9 to 19

Question 22

Find the probability P(z > -0.74) using the standard normal distribution.

A)0.2296
B)0.7704
C)0.7296
D)0.2600

Question 23

What is the special property of the standard normal distribution?

A)The mean is 0 and the standard deviation is 1.
B)The total area under the normal distribution curve is equal to 1.00.
C)The curve is continuous.
D)The mean is located at the center of the distribution.

Question 24

For a normal curve with mean 6 and standard deviation 3, which of the following parts of the normal curve will have an area of approximately 34%?

A)from 4.5 to 7.5
B)from 3 to 9
C)from 6 to 9
D)from 0 to 12

Question 25

For a normal distribution with mean 4 and standard deviation 4, the value 8 has a z value of

A)-1
B)1
C)2
D)3

Question 26

Find the probability P(z < -0.31) using the standard normal distribution.

A)0.6217
B)0.3783
C)0.8783
D)0.6900

Question 27

Find the probability P(z > 0.78) using the standard normal distribution.

A)0.2200
B)0.7823
C)0.7177
D)0.2177

Question 28

Find the probability P(Z < 0.22) using the standard normal distribution.

A)0.7800
B)0.4129
C)0.5871

Question 29

If a normal distribution has mean 16 and standard deviation 6, then

A)the median is 16 and the mode is 16
B)the median is 10 and the mode is 22
C)the median is 22 and the mode is 10
D)the median is 16 and the mode is 22

Question 30

One normal curve has mean 22 and standard deviation 4, a second normal curve has mean 4 and standard deviation 8.The curve that is more dispersed, or spread out, is

A)The first normal curve
B)The second normal curve
C)They are equally spread out
D)There is insufficient information to answer the question

Question 31

If the scores for a test have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.

A)4.75%
B)45.54%
C)42.07%
D)35.54%

Question 32

Find the probability P(0.21 < z < 1.28) using the standard normal distribution.

A)0.3166
B)0.6834
C)0.8166
D)0.4100

Question 33

For a normal distribution with mean -12 and standard deviation 4, the value -16 has a z value of

A)1
B)-3
C)-2
D)-1

Question 34

Find the area under the curve to the left of z = 1.69.

A)0.4545
B)0.4452
C)0.9545
D)0.9452

Question 35

Give the term for the number of standard deviations that a particular X value is away from the mean.

A)z value
B)discrete value
C)continuous value
D)y value

Question 36

In the figure below, what is the area under the curve between z = 1.50 and z = 2.50?

A)0.0802
B)0.0606
C)0.0764
D)1.00

Question 37

Find the area under the curve between z = -2.05 and z = 2.05.

A)0.4938
B)0.4798
C)0.9596
D)0.9876

Question 38

Using the normal distribution curve shown in the figure below, find the area under the curve between z = 0 and z = -2.16?

A)-0.4821
B)0.4821
C)-0.4846
D)0.4846

Question 39

Find the probability P(-0.77 < z < -0.16) using the standard normal distribution.

A)0.0400
B)0.7842
C)0.3458
D)0.2158

Question 40

Find the probability P(-1.09 < z < 1.06) using the standard normal distribution.

A)0.8410
B)0.2824
C)0.7175
D)0.6744

Question 41

What z value corresponds to 17% of the data between the mean and the z value?

A)1.25
B)0.44
C)0.52
D)2.10

Question 42

The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45.Assume that the distribution is normally distributed.If a worker at this fast food restaurant is
Selected at random, what is the probability that the worker earns more than $6.75?

A)28.77%
B)27.64%
C)42.07%
D)5.17%

Question 43

If X is a normal random variable with mean 5, and if the probability that X is more than 4.08 is .5910 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

A)4.00
B)2.67
C)2.00
D)1.00

Question 44

If X is a normal random variable with mean 4, and if the probability that X is less than 5.54 is .67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

A)1.75
B)3.50
C)4.20
D)12.25

Question 45

A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years.If a person in Africa is selected at random, what is the probability that the
Person will die before the age of 65?

A)94.52%
B)82.89%
C)94.95%
D)88.49%

Question 46

The average age of a vehicle registered in Canada is about 100 months.If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 102 and 104 months? Assume the
Standard deviation for the population is 15.

A)66.67%
B)15.71%
C)63.47%
D)75.82%

Question 47

The mean weight of loads of rock is 46.0 tons with a standard deviation of 10.0 tons.If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 42.00
Tons.Assume that the variable is normally distributed.

A)0.1151
B)0.3151
C)0.1551
D)0.4008

Question 48

The average gas consumption of a certain model car is 8.1 litres/100 km.If the gas consumption is normally distributed with a standard deviation of 0.2, find the probability that a car has a gas consumption
Between 8.08 and 8.13 litres/100 km.

A)0.10
B)0.16
C)0.20
D)0.22

Question 49

If X is a normal random variable with standard deviation 2.50, and if the probability that X is more than 5.95 is .1271 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.)

A)5.8
B)5.0
C)4.7
D)3.1

Question 50

In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a
Student needs to qualify for acceptance into the university?

A)1330
B)1400
C)1250
D)1100

Question 51

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years.If an employee is picked at random, what is the probability that the
Employee has worked at the store for over 10 years?

A)49.16%
B)99.16%
C)0.84%
D)0.54%

Question 52

The average height of flowering cherry trees in a nursery is 9.5 feet.If the heights are normally distributed with a standard deviation of 1.3, find the probability that a tree is less than 11.5 feet tall.

A)0.82
B)0.94
C)0.97
D)0.88

Question 53

The average number of mosquitoes in a stagnant pond is 60 per square meter with a standard deviation of 12.If 16 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 63.0 mosquitoes per square meter.Assume that the variable is normally
Distributed.

A)0.4587
B)0.1587
C)0.1107
D)-0.0013

Question 54

If the standard deviation of a population is 70 and we want the standard error (the standard deviation of the sample mean) to be 14, then we need to take

A)5 samples
B)25 samples
C)125 samples
D)625 samples

Question 55

If X is a normal random variable with mean 6 and standard deviation 3.0, then find the value x such that P(Z < x) is equal to .86, as shown below.(Note: the diagram is not necessarily to scale.)

A)9.24
B)7.32
C)6.66
D)6.00

Question 56

If the standard deviation of a population is 50 and we take a sample of size 25, then the standard error (the standard deviation of the sample mean) is

A)10.00
B)5.00
C)250.00
D)2.00

Question 57

If X is a normal random variable with mean 9 and standard deviation 2.5, then find the value x such that P(Z > x) is equal to .7054, as shown below.(Note: the diagram is not necessarily to scale.)

A)8.10
B)8.33
C)7.65
D)11.10

Question 58

The average length of crocodiles in a swamp is 12.5 feet.If the lengths are normally distributed with a standard deviation of 2.1, find the probability that a crocodile is more than 12 feet long.

A)0.51
B)0.53
C)0.57
D)0.59

Question 59

The average age of doctors in a certain hospital is 48.0 years old with a standard deviation of 6.0 years.If 25 doctors are chosen at random for a committee, find the probability that the mean age of those doctors
Is less than 48.60 years.Assume that the variable is normally distributed.

A)0.3085
B)0.5715
C)0.6675
D)0.6915

Question 60

If X is a normal random variable with standard deviation 3.00, and if the probability that X is less than 7.64 is .648 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.)

A)5.6
B)6.0
C)6.2
D)6.5

Question 61

Which of the following statements is correct?

A)The distribution of the values in a sample is called a sampling distribution.
B)The variability of sample means is never smaller than that of the population being sampled.
C)The larger the sample size is, the larger is the standard error of the mean.
D)The distribution of the values of a statistic over all possible samples of fixed size is called a sampling distribution.

Question 62

What is the z value such that 50% of the total area lies to the right of the curve in any normal distribution?

Question 63

The __________ is the difference between the sample measure and the corresponding population measure
due to the fact that the sample is not a perfect representation of the population.
________________________________________

Question 64

A biologist estimates that 60% of deer in the region carry a certain type of tick.For a sample of 300 deer selected at random, what is the chance that 186 or fewer deer have this tick?

A)0.8135
B)0.7782
C)0.7344
D)0.7290

Question 65

A(n) __________ is another term which can be used to describe an approximately bell shaped curve.
________________________________________

Question 66

The __________ correction factor is necessary if relatively large samples are taken from a small
population, because the sample mean will then more accurately estimate the population mean and there
will be less error in the estimation.
________________________________________

Question 67

Mrs.Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20
words per minute.The top 3% of the class is to receive a special award.What is the minimum number of
words per minute a student would have to read in order to get the award?

Question 68

Of the members of a Boy Scout troop, 15% have received their first aid badge.If 40 boy scouts are selected at random, find the probability that four or more will have the first aid badge?

A)86.65%
B)85.35%
C)36.65%
D)35.35%

Question 69

When the data values are evenly distributed about the mean, the distribution is said to be
__________.
________________________________________

Question 70

If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat?

A)12.64%
B)11.72%
C)50.34%
D)13.14%

Question 71

A(n) __________ is employed when a continuous distribution is used to approximate a discrete
distribution.
________________________________________

Question 72

The average diameter of sand dollars on a certain island is 4.00 centimeters with a standard deviation of 0.80 centimeters.If 25 sand dollars are chosen at random for a collection, find the probability that
The average diameter of those sand dollars is more than 3.824 centimeters.Assume that the variable is
Normally distributed.

A)0.8414
B)0.8483
C)0.8643
D)0.8611

Question 73

A television station estimates that 50% of college students watch the Super Bowl.For a sample of 200 students selected at random, what is the mean and variance of the number of students who watch this
Game?

A)Mean = 100.0, Variance = 7.07
B)Mean = 50.0, Variance = 7.07
C)Mean = 50.0, Variance = 50.00
D)Mean = 100.0, Variance = 50.00

Question 74

If one assumes that the gestational age is normally distributed with mean 270 days and standard deviation 16.5, what proportion of births would be considered pre-term (less than 37 weeks)?

A)0.18
B)0.25
C)0.33
D)0.75

Question 75

The standard deviation of a distribution is 20.If a sample of 225 is selected, what is the standard error of
the mean?

Question 76

The Canada Safety Council reported that 8% of Canadian drivers read while driving.If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading while driving.

A)1.96%
B)2.04%
C)6.56%
D)0.56%

Question 77

A(n) __________ is a distribution obtained by using the means computed from random samples of a
specific size taken from a population.
________________________________________

Question 78

If the length of country and western songs has mean 170 seconds and standard deviation 30 seconds, then the probability that a random selection of 16 songs will have mean length of 160.48 seconds or less is

A)0.8980
B)0.3980
C)0.1020
D)0.6020

Question 79

As the sample size n increases, the shape of the distribution of the sample means taken with replacement
from a population with mean and standard deviation of  will
approach a normal distribution.This distribution will have a mean of and a
standard deviation of . This statement summarizes the __________.
________________________________________

Question 80

What is the z value to the right of the mean such that 85% of the total area lies to the left of it as shown in
the figure below?