Deck 6: The Normal Distribution

Question 1

Which choice is another term that can be used to describe a normal distribution:

A) bell curve
B) independent variable
C) discrete distribution
D) negatively or positively skewed

Answer 1

A

Question 2

For a normal distribution curve with a mean of 9 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to
A probability of approximately 34%?

A) from 9 to 14
B) from 4 to 14
C) from 6.5 to 11.5
D) from -1 to 19

Answer 2

A

Question 3

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

Answer 3

symmetrical

Question 4

A) 0.9846
B) 0.4846
C) 0.3708
D) 2.1600

Question 5

Which of the following properties distinguishes the standard normal distribution from other normal distributions?

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

Question 6

Question 7

Question 8

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

Question 9

In applied statistics, it is the area under the normal distribution curve which is most
important, not the value of single points on the curve.

Question 10

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

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

Question 11

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

A) It is bimodal.
B) It is bell-shaped.
C) The mean, median, and mode are equal.
D) It is never negative.

Question 12

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

Question 13

If a normal distribution has a mean of 35 and a standard deviation of 10, then

A) the median is 35 and the mode is 35.
B) the median is 45 and the mode is
C) the median is 25 and the mode is 45.
D) the median is 35 and the mode is

Question 14

The number of standard deviations a particular X value is from the mean is commonly referred to as .

Question 15

One normal curve has a mean of 24 and a standard deviation of 3. A second normal curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed,
Or spread out, is

A) the second normal curve.
B) the first normal curve.
C) both; they are equally spread out.
D) neither; by definition,a normal curve shows no spread.

Question 16

On an easy test, the mean score was 96 out of a possible 100 points. The distribution of the test scores is likely to be

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

Question 17

For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probability of
Approximately 68%?

A) from 10 to 20
B) from 5 to 25
C) from 15 to 25
D) from 12.5 to 17.5

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

Question 20

Question 21

A) 0.6729
B) 0.3600
C) 0.8271
D) 0.3271

Question 22

A) 0.4772
B) 0.0228
C) 0.9772
D) 0.0114

Question 23

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

Question 24

A) -1.46
B) 1.46
C) 1.23
D) 0.07

Question 25

A) 0.5359
B) 0.4641
C) 0.6898
D) 0.3102

Question 26

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

Question 27

A) 0.3708
B) 0.4846
C) 0.9846
D) -2.1600

Question 28

Question 29

A) 0.57
B) 0.27
C) -0.79
D) 0.44

Question 30

A) -0.51
B) 1.33
C) 0.41
D) -0.22

Question 31

A) 0.3557
B) 0.1443
C) 0.6300
D) 0.6443

Question 32

A) 0.2823
B) 0.7177
C) 0.2177
D) 0.7823

Question 33

A) 0.4666
B) 0.0668
C) 0.4332
D) 0.9332

Question 34

A) 0.7173
B) 0.8407
C) 0.2827
D) 0.6741

Question 35

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

Question 36

Question 37

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

Question 38

A) 0.2946
B) 0.7946
C) 0.7054
D) 0.2054

Question 39

A) 0.4861
B) 0.0426
C) 0.9574
D) 0.5139

Question 40

A) 42.07%
B) 45.54%
C) 45.25%
D) 35.54%

Question 41

A bottler of drinking water fills plastic bottles with a mean volume of 1001 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What
Proportion of bottles have volumes less than 1001 mL?

A) 0.5000
B) 0.5438
C) 1.0000
D) 0.9772

Question 42

The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of
Institution, the salary is $90,330. If the standard deviation for the salaries of both genders
Is approximately $5200 and the salaries are normally distributed, find the 80th percentile
Salary for the male professors and for female professors, respectively.

A) $100,725 and $91,370
B) $103,845 and $944,490
C) $104,053 and $94,698
D) $95,265 and $85,910

Question 43

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

A) 6.75%
B) 35.54%
C) 45.25%
D) 4.75%

Question 44

A) 0.8408
B) 0.0735
C) 0.1592
D) 0.2327

Question 45

A) 0.1112
B) 0.8554
C) 0.6915
D) 0.8888

Question 46

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL. The fill volumes are normally distributed. What
Proportion of bottles have volumes between 992 mL and 998 mL?

A) 0.0808
B) 0.6452
C) 0.4207
D) 0.3399

Question 47

The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. 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) 5.2%
B) 28.8%
C) 42.1%
D) 27.6%

Question 48

The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is
More than 11 feet long.

A) 0.38
B) 0.12
C) 0.88
D) 0.62

Question 49

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, and the distribution is approximately normal.
If an employee is picked at random, what is the probability that the employee has worked
At the store for over 10 years?

A) 99.2%
B) 1.7%
C) 49.2%
D) 0.8%

Question 50

The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find
The probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon.

A) 0.107
B) 0.273
C) 0.287
D) 0.213

Question 51

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

Question 52

A) -0.99, 0.99
B) -1.13, 1.13
C) -1.07, 1.07
D) -1.24, 1.24

Question 53

A) -1.40
B) -1.01
C) -1.13
D) -0.87

Question 54

The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation
Of $103. Find the limits for the middle 50% of contributions.

A) $723 and $861
B) $766 and $818
C) $741 and $844
D) $758 and $826

Question 55

A) 1.0000
B) 0.7389
C) 0.1587
D) 0.8413

Question 56

A) 0.34
B) 0.61
C) 0.82
D) 0.52

Question 57

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.9 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a
Money-back guarantee that her 6-week poults will weigh at least a certain amount. What
Weight should she guarantee so that she will have to give her customer's money back
Only 1% of the time?

A) 3.58 lb
B) 4.02 lb
C) 4.47 lb
D) 4.92 lb

Question 58

A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What
Proportion of bottles have volumes greater than 999 mL?

A) 0.8051
B) 1.0000
C) 0.6293
D) 0.4443

Question 59

A) 0.0900
B) 0.3504
C) 0.7796
D) 0.2204

Question 60

A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 2010 square feet, find the maximum and minimum
Sizes of the homes the contractor should build. Assume that the standard deviation is 90
Square feet and the variable is normally distributed.

A) 1934.4 and 2085.6
B) 1929 and 2091
C) 2001 and 2019
D) 1894.8 and 2125.2

Question 61

A(n) is a distribution of means obtained from
samples of a specific size taken from a population.

Question 62

A) 8.92
B) 7.84
C) 11.89
D) 8.56

Question 63

A) 8.7
B) 7.5
C) 8.0
D) 9.6

Question 64

A) 8.14
B) 10.24
C) 7.00
D) 11.63

Question 65

The difference between a sample mean and the population mean may be referred to as .

A) the standard deviation
B) sampling error
C) skewness
D) the variance

Question 66

A) 2.0
B) 0.5
C) 1.0
D) 1.3

Question 67

A) 3.7
B) 2.1
C) 4.0
D) 5.2

Question 68

A) 0.5
B) -0.5
C) 1.5
D) 2.5

Question 69

Question 70

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness.
21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

Question 71

A) -3
B) -4
C) -2
D) 0

Question 72

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

A) 3
B) 9
C) 81
D) 27

Question 73

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

A) 11.0
B) 55.0
C) 2.2
D) 5.0

Question 74

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will
Build to satisfy the middle 80% of the market. Assume that the variable is normally
Distributed.

A) $230,900 and $256,100
B) $242,000 and $245,000
C) $230,000 and $257,000
D) $224,300 and $262,700

Question 75

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 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) 94.5%
B) 44.5%
C) 89.0%
D) 61.0%

Question 76

A) 4.00
B) 1.00
C) 2.40
D) 2.00

Question 77

Question 78

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability
That a tree is less than 12.5 feet tall.

A) 0.82
B) 0.96
C) 0.91
D) 0.73

Question 79

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam 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) 1250
B) 1100
C) 1330
D) 1400

Question 80