Cameron University Statistics & Probability Worksheet
3/27/22, 2:04 PMMyOpenMath
Continuous Distributions
Joao Guilherme Guercheski Duleba
Question 1
0/1 pt
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The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 20 minutes.
What is the probability that washing dishes tonight will take me between 12 and 13 minutes?
Give your answer accurate to two decimal places.
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Question 2
0/1 pt
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19
0/1 pt
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The values of a particular distribution are uniformly distributed between 6 and 11.
5
6
P (9 < x < 10)
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7
8
9
10
11
12
=
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Question 3
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Match each graph with its equation.
( x − 50 )

e
−
2
2 ⋅ 52
√2π ⋅ 5

e
−
( x − 40 )
2
2 ⋅ 52
a.
√2π ⋅ 5
−

e
( x − 45 )
2⋅6
2
2
25 30 35 40 45 50 55
√2π ⋅ 6
b.
30 36 42 48 54 60
c.
35 40 45 50 55 60 65
Question 4
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The heights of adult men in America are normally distributed, with a mean of 69.6 inches and a
standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed,
but with a mean of 64.6 inches and a standard deviation of 2.52 inches.
a) If a man is 6 feet 3 inches tall, what is his zscore (to two decimal places)?
z=
b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.
%
c) If a woman is 5 feet 11 inches tall, what is her zscore (to two decimal places)?
z=
d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.
%
e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a
meaningful sentence.
Question 5
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The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and
standard deviation of 17 .
Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.
a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer
rounded to two decimal places.
%
b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the
nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and
down if there’s an issue!
people
c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US
qualify for stage 1?
%
d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your
systolic BP? Round to 2 decimal places.
lbs
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Question 6
0/1 pt
3
19
In a normal distribution, a data value located 0.7 standard deviations below the mean has Standard
Score: z =
In a normal distribution, a data value located 1.9 standard deviations above the mean has Standard
Score: z =
In a normal distribution, the mean has Standard Score: z =
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Question 7
0/1 pt
If the area to the left of
x
3
19
3
19
in a normal distribution is 0.749, what is the area to the right of x?
Answer:
If the area to the right of
x
in a normal distribution is 0.749, what is the area to the left of x?
Answer:
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Question 8
0/1 pt
A variable is normally distributed with mean 23 and standard deviation 7. Use your graphing calculator
to find each of the following areas. Write your answers in decimal form. Round to the nearest
thousandth as needed.
a) Find the area to the left of 24.
b) Find the area to the left of 21.
c) Find the area to the right of 23.
d) Find the area to the right of 25.
e) Find the area between 21 and 27.
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Question 9
0/1 pt
3
19
Find the area of the shaded region under the standard normal distribution to the left of the given zscore. Round your answer to four decimal places.
4
P (z <
3
2
z = 2.39
1
0
z
1
2
3
4
− 2.39) =
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Question 10
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Find the area of the shaded region under the standard normal distribution to the right of the given zscore. Round your answer to four decimal places.
4
3
2
z = 2.49
P (z >
1
0
z
1
2
3
4
− 2.49) =
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Question 11
0/1 pt
3
19
Find the area of the shaded region under the standard normal distribution between the given zscores.
Round your answer to four decimal places.
4
3
2
1
0
0.35
z
1
0.84
2
3
4
P( – 0.35 < z < 0.84) =
Video
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Question 12
0/1 pt
3
19
Find the zscore for the given shaded region under the standard normal distribution. Round your answer
to two decimal places.
Shaded Area = 0.7
4
3
2
1
0
z
1
2
3
4
zscore =
Question 13
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Q
p
Find the zscore for the given shaded region under the standard normal distribution. Round your answer
to two decimal places.
Shaded Area = 0.6
4
3
2
1
0
z
1
2
3
4
zscore =
Question 14
0/1 pt
3
19
Use the given shaded area (0.0973) in the middle of the standard normal distribution and the given zscore (2.06) to find the missing zscore. The shaded region is not symmetric about `z=0`. Round your
final answer to two decimal places.
Shaded Area = 0.0973
4
3
2
2.06
1
?
0
z
1
2
3
4
Upper zscore =
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Question 15
0/1 pt
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Adult male height is normally distributed with a mean of 69.1 inches and a standard deviation of 2.33
inches. If an adult male is randomly selected, what is the probability that the adult male has a height
less than 73.3 inches? Round your final answer to four decimal places.
Question 16
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The graph illustrates a normal distribution for the prices paid for a particular model of HD television.
The mean price paid is $1400 and the standard deviation is $140. Round answers to at least 4 decimal
places, use technology.
980
1120
1260 1400 1540
Distribution of Prices
1680
1820
What is the probability that a buyer paid between $1260 and $1540?
What is the probability that a buyer paid between $1400 and $1680?
What price would the buyer pay to get 9% the most expensive HD televisions?
$
Question 17
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The incubation times for Rhode Island Red chicks is approximately normally distributed with a mean of
20.4 days and standard deviation of 0.8 days.
1. Determine the proportion of Rhode Island Red chicks that have incubation times less than 18.5
days. Round your answer to 4 decimal places.
2. The fastest hatching 20 percent of Rhode Island Red chicks have incubation times of _____ days or
less. Note, the fastest hatching have shorter incubation times and arrive in less than 20.4 days.
Round your answer to 1 decimal place.
3. The middle 90 of Rhode Island Red chicks have incubation times between _____ and _____ days.
Round your answers to 1 decimal place.
4. Determine the proportion of Rhode Island Red chicks have incubation times between 19 and 21.6
days. Round your answer to 4 decimal places.
5. Determine the proportion of Rhode Island Red chicks have incubation times greater than 21.6
days. Round your answer to 4 decimal places.
6. The slowest hatching 15 percent of Rhode Island Red chicks have incubation times of _____ days
or more. Note, the slowest hatching have longer incubation times and require more than 20.4
days to arrive. Round your answer to 1 decimal place.
Question 18
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The number of chocolate chips in a popular brand of cookie is normally distributed with a mean of 20
chocolate chips per cookie and a standard deviation of 2.6 chips. When the cookies come out of the
oven, only the middle 90% in terms of the number of chocolate chips are acceptable (the rest are
considered defective). What are the cutoff numbers for the number of chocolate chips in acceptable
cookies? (Give your answers to three decimal places)
and
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