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PS22 Quiz 6.2

Total questions: 80

Worksheet time: 3hrs 41mins

Name
Class
Date
1.

What is the total area under the normal curve in a standard normal distribution?

a)

1

b)

2

c)

3

d)

4

2.

For the density curve shown, which statement is true?

a)

The density curve is Normal.

b)

The density curve is skewed right.

c)

At the mean, the height of the curve is 1.

d)

The density curve is symmetric

e)

None of the above is correct.

3.

For the density curve shown, which statement is true?

a)

The mean is greater than the median.

b)

The mean is less than the median.

c)

The mean and median are equal.

d)

The mean could be either greater than or less than the median.

e)

None of the above is correct.

4.

Two measures of center are marked on the density curve shown. Which of the following is correct?

a)

The median is at the yellow line and the mean is at the red line.

b)

The median is at the red line and the mean is at the yellow line.

c)

The mode is at the red line and the median is at the yellow line.

d)

The mode is at the yellow line and the median is at the red line.

e)

.

The mode is at the red line and the mean is at the yellow line.

5.

The density curve shown takes the value 0.5

on the interval 0 ≤ x ≤ 2 and takes the value 0

everywhere else. What percent of the observations lie

between 0.5 and 1.2?

a)

25%

b)

35%

c)

50%

d)

68%

e)

70%

6.
A z-score tells you...
a)
the standard deviation of a sampling distribution.
b)
the original raw score on which it is based.
c)
if the distribution it comes from is normal.
d)
how many standard deviations away from the mean a score lies.
7.
Find the area under the standard normal curve to the right of z = -2.67.
a)
0.0869
b)
0.9962
c)
0.0008
d)
0.1234
8.
Find the area under the normal distribution curve to the left of 
Z=0.27.
a)
0.3936
b)
0.3897
c)
0.6064
d)
0.4892
9.
Find the area under the normal distribution curve between 
z=-1.53 and z=0.
a)
0.437
b)
0.563
c)
0.500
d)
0.063
10.
Find the area under the normal distribution curve between a z=-1.26 and z=.57. 
a)
0.0047
b)
0.9204
c)
0.6119
d)
0.4981
11.
Adam's Z-score on a test is +2.5.  What does this mean?
a)
He'd better start studying.
b)
He did better than EVERYONE.
c)
He scored 2.5 standard deviations above the average.
d)
He did terrible.
12.
If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?
a)
-1.25
b)
+1.25
c)
+1.20
d)
+1.02
13.
Find the area of the shaded region if the z-score is 0.75
a)
0.2266
b)
0.7734
c)
0.758
d)
0.242
14.
What is the the total area under the standard normal distribution curve?
a)
100
b)
25
c)
.5
d)
1
15.
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?
a)
68%
b)
34%
c)
16%
d)
2.5%
16.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
17.

What is the the total area under the standard normal distribution curve?

a)

100

b)

25

c)

.5

d)

1

18.
The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?
a)
0.6915
b)
0.1762
c)
0.8238
d)
-0.93
19.
The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?
a)
-1.33
b)
1.33
c)
0.88
d)
1.02
20.
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
21.
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?
a)
92.4%
b)
10.5%
c)
16%
d)
7.6%
22.
The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?
a)
115
b)
130.75
c)
145
d)
120
23.
The z-score represents.....
a)
the amount of standard deviations a data value is above or below the mean.
b)
the percentile the data value is above or below the mean.
c)
the amount of standard deviations a data value is above or below the median.
d)
the percent the data value is above or below the mean.
24.
The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?
a)
0.67 inch
b)
263 inches
c)
272.44 inches
d)
277.25 inches
25.
Which is NOT true about the standard normal distribution?
a)
It is bell-shaped.
b)
It is unimodal.
c)
The mean is 0 and the standard deviation is 1.
d)
It is asymmetrical.
26.
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?
a)
68%
b)
34%
c)
16%
d)
2.5%
27.

If I tell you that you scored at the 55th percentile on your final exam, you would know:

a)

55% of the class scored the same or worse than you did

b)

You earned a 55% on the exam

c)

You failed the exam

d)

45% of the class scored worse than you did

28.
The 75th percentile is also know as the
a)
median
b)
third quartile
c)
1st quartile`
d)
interquartile range
29.

Find the z-score for 48 given a mean of 50 and a standard deviation of 5.

a)

2.5

b)

-2.5

c)

-0.4

d)

0.4

30.

Find the area under the standard normal curve that lies to the left of z=2.1.

a)

1.79%

b)

-1.79%

c)

98.21%

d)

0.98%

31.

Find the area under the standard normal curve that lies to the right of z=-0.67.

a)

63.42%

b)

74.86%

c)

25.14%

d)

50%

32.

Test has a mean of 40 and a standard deviation of 10. What is the percent of people that scored above 62?

a)

1.39%

b)

45.34%

c)

98.41%

d)

22.34%

33.

A continuous random variable is normally distributed with mean 145 and standard deviation is 5. Find P(136<X<140).

a)

0.8054

b)

0.8772

c)

0.1228

d)

0.1587

34.

The width of the curve is determined by the _____________________.

a)

Mean

b)

Variation

c)

Standard Deviation

d)

Standard Normal Curve

35.

A standard normal curve is a normal probability distribution that has a standard deviation of ____ and a mean of ____.

a)

1, 0

b)

0, 1

c)

0, 0

d)

1, 1

36.

A normal distribution is symmetric.

a)

True

b)

False

37.

The normal probability distribution is completely described by its mean and ________.

a)

variance

b)

standard deviation

c)

range

d)

mean deviation

38.

The standard normal probability distribution has mean of 0 and a standard deviation of _____.

a)

12\frac{1}{2}

b)

−1-1

c)

11

d)

−12-\frac{1}{2}

39.

Any normal probability distribution can be converted to the standard normal probability distribution by the following formula

a)

z=X−μσz=\frac{X-\mu}{\sigma}

b)

z=μ−Xσz=\frac{\mu-X}{\sigma}

c)

z=X+μσz=\frac{X+\mu}{\sigma}

d)

z=Xμσz=\frac{X\mu}{\sigma}

40.

By standardizing a normal probability distribution, we can report the distance of a value from the mean in units of the __________ .

a)

median

b)

standard deviation

c)

variance

d)

mode

41.

The signed distance between a selected value, designated X, and the mean, μ, divided by the standard deviation, σ.

a)

p value

b)

z value

c)

r value

d)

t value

42.

It was reported that the weekly income of Uber drivers followed the normal distribution with a mean of $1,000

and a standard deviation of $100. What is the z value corresponding to to x = $1,000?

a)

1

b)

-1

c)

0

d)

cannot be determined

43.

It was reported that the weekly income of Uber drivers followed the normal distribution with a mean of $1,000

and a standard deviation of $100. What is the z value corresponding to to x = $1,100?

a)

1

b)

-1

c)

0

d)

cannot be determined

44.

The distribution of weekly incomes follows the normal probability distribution, with a mean of $1,000 and a standard deviation of $100. What is the sign of the z value corresponding to an income of $750?

a)

negative

b)

positive

45.

The distribution of weekly incomes follows the normal probability distribution, with a mean of $1,000 and a standard deviation of $100. What is the sign of the z value corresponding to an income of $1,200?

a)

negative

b)

positive

46.
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?
a)
68%
b)
34%
c)
16%
d)
2.5%
47.
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?
a)
68%
b)
34%
c)
16%
d)
2.5%
48.
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.
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.
49.
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.
50.
Roger bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Roger's scores?
a)
193
b)
127
c)
60
d)
66
51.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
52.
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
53.
What does the mean tell you about a data set
a)
It tells you the number that occurs the most
b)
It is the difference between the highest and lowest number
c)
It tells you the average of the data set
d)
It tells you how mad someone is at another persom
54.
What is the Normal Range (68%) of the annual precipitation for Phoenix, if the average is 29 with a standard deviation of 3?
a)
26-32
b)
3-29
c)
26-29
d)
39-32
55.
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
56.
The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?
a)
0.67 inch
b)
263 inches
c)
272.44 inches
d)
277.25 inches
57.
The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. What percent of men are between 64 and 66.5 inches tall? 
a)
50%
b)
2.5%
c)
13.5%
d)
34%
58.
The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Between what heights do the middle 95% of men fall? 
a)
66.5-71.5
b)
64-74
c)
61.5-76.5
d)
65-73
59.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are between 75 and 82?

a)

68%

b)

81.5%

c)

16%

d)

34%

60.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are above 82?

a)

34%

b)

81.5%

c)

16%

d)

2.5%

61.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are between 54 and 96?

a)

34%

b)

99.7%

c)

95%

d)

2.5%

62.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are greater than 68?

a)

34%

b)

84%

c)

95%

d)

68%

63.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 61 and 89?

a)

475

b)

400

c)

340

d)

80

64.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 82?

a)

475

b)

170

c)

237

d)

80

65.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 75 and 82?

a)

475

b)

170

c)

340

d)

237

66.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 68 and 82

a)

11

b)

2

c)

340

d)

498

67.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 89?

a)

11

b)

12

c)

36

d)

237

68.

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 68?

a)

11

b)

12

c)

420

d)

250

69.

What type of distribution is pictured?

a)

Right skewed

b)

Left skewed

c)

Random

d)

Normal

70.

What is P(x > 27)?

a)

97.5%

b)

84%

c)

13.5%

d)

2.5%

71.

What is P(33 < x < 51)?

a)

84%

b)

68%

c)

81.5%

d)

18.5%

72.

What is P(x < 35)

a)

47.5%

b)

13.5%

c)

84%

d)

16%

73.

What is P(68 < x < 84)?

a)

47.5%

b)

83.85%

c)

84%

d)

87.5%

74.

What is P( x < 88)?

a)

13.5%

b)

2.5%

c)

97.5%

d)

95%

75.

A statistical study calculated that the average cost of used iPhones is $230, with a standard deviation of $25. What is the probability that a select phone from the sample costs between $205 and $280?

a)

81.5%

b)

68%

c)

95%

d)

47.5%

76.

A statistical study calculated that the average usage of smartphones during class is 22 minutes a day, with a standard deviation of 5 minutes. What is the percentage of the people from the study that uses their smartphones less than 27 minutes a day?

a)

34%

b)

16%

c)

84%

d)

95%

77.

A statistical study calculated that the average score on the SAT Exam is 1270, with a standard deviation of 130. What percentage of examinees from the study scored between 1270 and 1530?

a)

84%

b)

68%

c)

97.5%

d)

47.5%

78.

A statistical study calculated that the average time teenagers spend playing app games each day is 3.4 hours, with a standard deviation of 0.7 hours. What is the percentage of teenagers in the study that spends less than 2.7 hours each day on app games?

a)

68%

b)

16%

c)

84%

d)

13.5%

79.

A statistical study calculated that the average speed of bus drivers is 38 mph, with standard deviation of 4 mph. What percentage of bus drivers in the study drive an average speed greater than 46 mph?

a)

97.5%

b)

84%

c)

16%

d)

2.5%

80.

A standard normal curve is a normal probability distribution that has a standard deviation of ____ and a mean of ____.

a)

1, 0

b)

0, 1

c)

0, 0

d)

1, 1

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