- One of the side effects of flooding a lake in northern boreal forest areas (e.g. for a
hydro-electric project) is that mercury is leached from the soil, enters the food chain,
and eventually contaminates the fish. The concentration in fish will vary among
individual fish because of differences in eating patterns, movements around the lake,
etc. Suppose that the concentrations of mercury in individual fish follows an
approximate normal distribution with a mean of 0.25 ppm and a standard deviation of
0.08 ppm. Fish are safe to eat if the mercury level is below 0.30 ppm. What
proportion of fish are safe to eat?
- 63%
- 23%
- 73%
- 27%
- 37%

- Refer to the previous question.
The Department of Fisheries and Oceans wishes to know the mercury
level of the top 20% of the fish.
The appropriate percentile and mercury level for this lake is:
- 20
th percentile has a value of -0.84 ppm - 20
th percentile has a value of 0.18 ppm - 80
th percentile has a value of 0.32 ppm - 80
th percentile has a value of 0.84 ppm - 20
th percentile has a value of 0.07 ppm

- 20
- The following graph is a normal probability plot for the amount of rainfall in acre-feet
obtained from 26 randomly selected clouds that were seeded with silver oxide:

- The data appear to show exponential growth; that is, the amount of rainfall increases exponentially as the amount of silver oxide increases.
- The pattern suggests that the measurement is not normally distributed.
- A least squares regression line should be fitted to the rainfall variable.
- It can be expected that the histogram of rainfall amount will look like the normal curve.
- The shape of the curve suggests that rainfall is caused by seeding the clouds with silver oxide.

- Marks on a Chemistry test follow a normal distribution with a mean of 65 and a
standard deviation of 12. Approximately what percentage of the students have
scores below 50?
- 11%
- 89%
- 15%
- 18%
- 39%

- Refer to the preceding question. What is the approximate 90th percentile of the mark
distribution?
- 80
- 90
- 85
- 75
- 95

- The marks on a statistics test are normally distributed with a mean of 62 and a
variance of 225. If the instructor wishes to assign B's or higher to the top 30% of the
students in the class, what mark is required to get a B or higher?
- 68.7
- 71.5
- 73.2
- 74.6
- 69.9

- The grade point averages of students at the University of Manitoba are approximately
normally distributed with mean equal to 2.4 and standard deviation equal to 0.8. What
fraction of the students will possess a grade point average in excess of 3.0 ?
- .7500
- .6000
- .2734
- .2500
- .2266

- In some courses (but certainly not in an intro stats course!), students are graded on a "normal curve". For example,
students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and
1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5 standard
deviations above the mean receive a B; between 1.5 and 2.0 standard deviations above
the mean receive a B+, etc. The class average in an exam was 60 with a standard
deviation of 10. The bounds for a B grade and the percentage of students who will
receive a B grade if the marks are actually normal distributed are:
- (65, 75), 24.17%
- (70, 75), 18.38%
- (70, 75), 9.19%
- (65, 75), 12.08%
- (70, 75), 6.68%

Refer to the previous question. Another Instructor decides that the lower "B" cutoff should be the 70th percentile. The lower-cutoff for a B grade is:

- 70
- 65
- 60
- 75
- 80

- The diameters of steel disks produced in a plant are normally distributed with a mean
of 2.5 cm and standard deviation of .02 cm. The probability that a disk picked at
random has a diameter greater than 2.54 cm is about:
- .5080
- .2000
- .1587
- .0228
- .4920

- Suppose the test scores of 600 students are normally distributed with a mean of 76
and standard deviation of 8. The number of students scoring between 70 and 82 is:
- 272
- 164
- 260
- 136
- 328

- Bolts that are used in the construction of an electric transformer are supposed to be
0.060 inches in diameter, and any bolt with diameter less than 0.058 inches or greater
than 0.062 inches must be scrapped. The machine that makes these bolts is set to
produce bolts of 0.060 inches in diameter, but it actually produces bolts with
diameters following a normal distribution with µ=0.060 inches and =0.001 inches.
The proportion of bolts that must be scrapped is equal to:
- 0.0456
- 0.0228
- 0.9772
- 0.3333
- 0.1667

- The cost of treatment per patient for a certain medical problem was modeled by one
insurance company as a normal random variable with mean $775 and standard
deviation $150. What is the probability that the treatment cost of a patient is less than
$1,000, based on this model?
- .5000
- .6826
- .8531
- .9332
- Cannot be computed without knowledge of additional parameters

- The time that a skier takes on a downhill course has a normal distribution with a mean
of 12.3 minutes and standard deviation of 0.4 minutes. The probability that on a
random run the skier takes between 12.1 and 12.5 minutes is:
- 0.1915
- 0.3830
- 0.3085
- 0.6170
- 0.6826

- It is known that the resistance of carbon resistors is normally distributed with
µ=1200 ohms and = 120 ohms. What proportion of the resistors have resistances
that differ from the mean resistance by more than 120 ohms?
- 0.9544
- 0.3413
- 0.1587
- 0.6826
- 0.3174

- The time required to assemble an electronic component is normally distributed with a
mean of 12 minutes and a standard deviation of 1.5 min. Find the probability that a
particular assembly takes more than 14.25 minutes.
- .9332
- .0668
- .3413
- .4332
- .1587

- Heights of males are approximately normally distributed with a mean of 170 cm and
a standard deviation of 8 cm. What fraction of males are taller than 176 cm?
- .7500
- .6000
- .2734
- .2500
- .2266

- The height of an adult male is known to be normally distributed with mean of 175 cm
and standard deviation 6 cm. The 20th percentile of the distribution of heights is:
- 175
- 179
- 170
- 172
- 174

- The heights of students at a college are normally distributed with a mean of 175 cm
and a standard deviation of 6 cm. One might expect in a sample of 1000 students that
the number with heights less than 163 cm is:
- 997
- 23
- 477
- 228
- 456

- The height of an adult male is known to be normally distributed with a mean of 69
inches and a standard deviation of 2.5 inches. The height of the doorway such that 96
percent of the adult males can pass through it without having to bend is:
- 1.75
- 64.63
- 73.38
- 79.94
- 58.06

- The distribution of weights in a large group is approximately normally distributed.
The mean is 80 kg. and approximately 68% of the weights are between 70 and 90 kg.
The standard deviation of the distribution of weights is equal to:
- 20
- 5
- 40
- 50
- 10

- The distribution of weights of a large group of high school students is normally
distributed with µ=55 kg and =5 kg. Which of the following is true?
- About 16 percent of the students will be over 60 kg.
- About 2.5 percent will be below 45 kg.
- Half of them can be expected to weigh less than 55 kg.
- About 5 percent will weigh more than 63 kg.
- All the above are true.

- The daily milk production of Guernsey cows is approximately normally distributed
with a mean of 35 kg/day and a std. deviation of 6 kg/day. The probability that a days
production for a single animal will be less than 28 kg. is approximately:
- .41
- .09
- .38
- .12
- .62

- Refer to the previous question. The producer is concerned when the milk production
of a cow falls below the 5th percentile since the animal may be ill. The 5th percentile
(in kg) of the daily milk production is approximately:
- 1.645
- -1.645
- 33.36
- 25.13
- 44.87

- Which of the following is NOT CORRECT about a standard normal distribution?
- P( 0 < Z < 1.50) = .4332
- P( Z < -1.0 ) = .1587
- P( Z > 2.0 ) = .0228
- P( Z < 1.5 ) = .9332
- P( Z > -2.5) = .4938

- The measurement of the width of the index finger of a human right hand is a normally
distributed variable with a mean of 6 cm. and a standard deviation of 0.5 cm. What is
the probability that the finger width of a randomly selected person will be between 5
cm. and 7.5 cm.?
- .9759
- .0241
- .9500
- 1.000
- not within ± 0.001 of these

## Normal approx. to binomial

- The National Broomball League claims to have a balanced league; that is,
for any given game each team has an equal chance of winning or losing with no ties.
Assuming the claim is true, what is the approximate probability that a given team will
lose more than 61 games out of the 100 played?
- 0.0500
- 0.4918
- 0.0107
- 0.0082
- 0.0164

- The probability of getting a parking ticket when not paying for a 2-hour period is 0.3.
What is the probability of getting at least 60 tickets if you park on 250 occasions for a
2-hour period and don't pay?
- 0.016
- 0.019
- 0.98
- 0.93
- 0.072

- A professional basketball player sinks 80% of his foul shots, in the long run. If he
gets 100 tries during a season, then the probability that he sinks between 75 and 90
shots (inclusive) is approximately equal to:
- Pr ( -1.25 <= Z <= 2.5 )
- Pr ( -1.125 <= Z <= 2.625 )
- Pr (-1.125 <= Z <= 2.375 )
- Pr ( -1.375 <= Z <= 2.375 )
- Pr (-1.375 <= Z <= 2.625 )

- Suppose in the University of Manitoba, 30% of the students live in apartments. If 200
students are randomly selected, then the probability that the number of them living in
apartments will be between 50 and 75 inclusive, is:
- .9167
- .9298
- .9390
- .9268
- .9208

- If X has a binomial distribution with n = 400 and p = .4, the approximate
probability of the event {155 < X < 175} is:
- 0.6552
- 0.6429
- 0.6078
- 0.6201
- 0.6320

- If in the previous question we change the interval to 155 <= X <= 175, the approximate
probability is;
- 0.4
- larger than that in the previous question
- smaller than that in the previous question
- equal to that in the previous question
- may be smaller or larger than that in the previous question

- Companies are interested in the demographics of those who listen to the radio
programs they sponsor. A radio station has determined that only 20% of listeners
phoning in to a morning talk program are male. During a particular week, 200 calls
are received by this program. What is the approximate probability that at least 50 of
the callers are male?
- .0466
- .0212
- .1168
- .1402
- Not within ± .01 of any of the above.

- The unemployment rate in a certain city is 8.5%. A random sample of 100 people
from the labour force is drawn. Find the approximate probability that the sample
contains at least ten unemployed people.
- .3879
- .3245
- .3419
- .2946
- .3594

- A politician has targeted 100 homes to visit during a week. From past experience, 50
percent of the households answer the bell and invite him in. Of this, 80 percent will
agree with his policies. The approximate probability that the politician will get support
from at least 45 households during a week is:
- 0.1991
- 0.3212
- 0.8643
- 0.1376
- 0.1788

- People who have been in contact with a carrier of a disease, have a 40% chance of
contracting the disease. Suppose that the carrier of the diseases may have infected a
school with 500 people. Find the approximate probability that at least 215 people will
contract the disease.
- .09
- .91
- between .05 and .34
- 1.37
- between 2.5% and 17%

These problems were captured from the Simon Fraser University web site, and moved here for efficiency. We are greatful to the original authors.