Basic Stat HW Ch 6
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HWChapter6.docxPractice Questions Chapter 6
Part 1 Normal Distribution
1. Let z be a standard normal random variable. Find
a. P (z < 2.35)
b. P (z > 1.64)
c. P (z <-1.98)
d. P (z >- 1.73)
e. P (z = 0.43)
f. P (1.51 ≤ z ≤ 2.14)
g. P (-2.14 ≤ z < 1.47)
h. P (-2.72 < z < - 1.37)
2. Assume that weight of a person is normally distributed with mean 70kg and standard deviation 10
a. Find the probability that a randomly selected person is Less than 50 kg.
b. Find the probability that a randomly selected person is More than 85 kg
c. Find the probability that a randomly selected person is More than 60kg but less than 90 kg
3. Statistically it is shown that the temperature in a city is normally distributed with mean 12°C and standard deviation 6° C.
a. Find the probability that at random day the temperature will be less than 20°C.
b. Find the probability that at random day the temperature will be greater than 10°C.
c. The temperature will be between 8°C and 15°C.
4.
a. What is the probability that a randomly selected vitamin will contain less 80 grams of pyridoxine?
b. What is the probability that a randomly selected vitamin will contain at least than 55 grams of pyridoxine?
c. What is the probability that a randomly selected vitamin will contain between 63 and 74 grams of pyridoxine?
d. What is the probability that a randomly selected vitamin will exactly 75 grams of pyridoxine?
5. The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.
a. What is the probability that a product is assembled in less than 12 minutes?
b. What is the probability that a product is assembled in between 12 and 16minutes?
c. What is the probability that a product is assembled in exactly 12 minutes?
6.
a. What is the probability that a randomly selected vitamin will contain less than 82 grams of pyridoxine?
b. What is the probability that a randomly selected vitamin will contain more100 grams of pyridoxine?
c. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine?
7. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute.
a. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
b. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in more than 3 minutes.
c. Find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.
8. The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces.
a. What is the probability that a randomly selected can will contain less than 7.8 ounces?
b. What is the probability that a randomly selected can will contain more than 8.4 ounces of tomato paste?
c. What is the probability that a randomly selected can will contain between 7.4 and 8.2 ounces?
9. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce.
a. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.
b. Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.
Part 2 Uniform Distribution
10. Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 10 to 80 minutes.
a. What is the mean of the time interval?
b. What is the variance and the standard deviation of the time interval?
c. What is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?
d. What is the probability that the time interval between two consecutive defective light bulbs will be less than 20 minutes?
11. Assume that waiting time in a restaurant is uniformly distributed between 6 and 14 minutes.
a. Write the probability density function
b. What is the probability that a customer waits More than 10 Minutes?
c. What is the probability that a customer waits Exactly 10 minutes?
d. What is the probability that a customer waits Not more than 9 minutes?
e. What is the probability that a customer waits Between 8 and 20 minutes?
f. Find the average waiting time?
g. Find the Variance and standard deviation of waiting time?
12. Arrival time of a plane is uniformly distributed between 15 and 45 minutes.
a. Find Mean and standard deviation of arrival time.
b. Write the probability density function and graph it.
c. What is the probability that the next plane will arrive after 20 minutes?
d. What is the probability that the next plane will arrive after 10 minutes?
e. What is the probability that the next plane will arrive after 50 minutes?
f. What is the probability that the next plane will arrive between 20 and 60 minutes?
13. Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 40 to 110 minutes.
a. Find the probability density function.
b. What is the mean and variance of the time interval?
c. What is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?
d. What is the probability that the time interval between two consecutive defective light bulbs will be less than 35 minutes?
e. What is the probability that the time interval between two consecutive defective light bulbs will be between 45 and 100 minutes?
14. Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes.
a. Find the probability density function
b. What are the mean and the variance of the time interval?
c. What is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?
d. What is the probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes?
e. What is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 20 minutes?
f. What is the probability that the time interval between two consecutive defective light bulbs will be at least 80 minutes?
15. The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.
a. Find the probability density function.
b. Compute the probability that a student will take between 45 and 50 minutes to complete the examination.
c. Compute the probability that a student will take less than 40 minutes to complete the examination.
d. Compute the probability that a student will take exactly 50 minutes to complete the examination.
16. Assume that the waiting time for an elevator is uniformly distributed and varies between 0 and 6 minutes.
a. Write the probability density function.
b. Compute the probability that you will wait between 3 and 4.5 minutes.
c. Compute the probability that you will wait more than 6 minutes
d. Compute the probability that you will wait exactly 3 minutes.
m
s
Practice Questions Chapter
6
Part 1
Normal Distribution
1.
Let z be a standard normal random variable. Find
a.
P (z < 2.35
)
b.
P (z > 1.64
)
c.
P (z <
-
1.98
)
d.
P (z >
-
1.73
)
e.
P (z = 0.43
)
f.
P (1.51
=
z
=
2.14
)
g.
P (
-
2.14
=
z < 1.47
)
h.
P (
-
2.72 < z <
-
1.37
)
2.
Assume that weight
of a person is normally distributed with mea
n 70kg and standard deviation 1
0
a.
Find the probability that a randomly selected person is
Less
than 50 kg.
b.
Find the probability that a
randomly selected person is More
than 85 kg
c.
Find the probability that a
randomly selected person is More than 60kg but less than 90 kg
3.
Statistically it is shown that the temperature in a city is normally distributed with mean 12°C and standard
deviation 6° C.
a.
Find the probability that at random day the temperature will be
less than 20°C.
b.
Find the probability that at random day the temperature will be greater than 10°C.
c.
The temperature will be between 8°C and 15°C.
4.
The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with
m
= 70 grams and
s
= 15 grams.
a.
What is the probability that a randomly select
ed vitamin will
contain less
80 grams of pyridoxine?
b.
What is the probability that a randomly selected vitamin will contain
at least
than 55 grams of pyridoxine?
c.
What is the probability that a randomly selected vitamin will contain between 63 and 74 grams of
pyridoxine?
d.
What is the probability that a randomly selected vitamin will exactly 75 grams of pyridoxine?
5.
The amount of time necessary for assembly line wo
rkers to complete a product is a normal random variable
with a mean of 15 minutes and a standard deviation of 2 minutes.
a.
What is the probability that a product is assembled in less than 12 minutes?
b.
What is the probability that a product is assembled in
between 12 and 16minutes?
c.
What is the probability that a product is assembled in exactly 12 minutes?
6.
The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with
m
= 110 grams and
s
= 25
grams.
a.
What is the probability that a randomly selected vitamin will contain
less than 82
grams of pyridoxine?
b.
What is the probability that a randomly s
elected vitamin will contain more
100 grams of pyridoxine?
c.
What is the probability that a randomly selec
ted vitamin will contain between 100 and 120 grams of
pyridoxine?
Practice Questions Chapter 6
Part 1 Normal Distribution
1. Let z be a standard normal random variable. Find
a. P (z < 2.35)
b. P (z > 1.64)
c. P (z <-1.98)
d. P (z >- 1.73)
e. P (z = 0.43)
f. P (1.51 = z = 2.14)
g. P (-2.14 = z < 1.47)
h. P (-2.72 < z < - 1.37)
2. Assume that weight of a person is normally distributed with mean 70kg and standard deviation 10
a. Find the probability that a randomly selected person is Less than 50 kg.
b. Find the probability that a randomly selected person is More than 85 kg
c. Find the probability that a randomly selected person is More than 60kg but less than 90 kg
3. Statistically it is shown that the temperature in a city is normally distributed with mean 12°C and standard
deviation 6° C.
a. Find the probability that at random day the temperature will be less than 20°C.
b. Find the probability that at random day the temperature will be greater than 10°C.
c. The temperature will be between 8°C and 15°C.
4. The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 70 grams and
= 15 grams.
a. What is the probability that a randomly selected vitamin will contain less 80 grams of pyridoxine?
b. What is the probability that a randomly selected vitamin will contain at least than 55 grams of pyridoxine?
c. What is the probability that a randomly selected vitamin will contain between 63 and 74 grams of
pyridoxine?
d. What is the probability that a randomly selected vitamin will exactly 75 grams of pyridoxine?
5. The amount of time necessary for assembly line workers to complete a product is a normal random variable
with a mean of 15 minutes and a standard deviation of 2 minutes.
a. What is the probability that a product is assembled in less than 12 minutes?
b. What is the probability that a product is assembled in between 12 and 16minutes?
c. What is the probability that a product is assembled in exactly 12 minutes?
6. The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and
= 25 grams.
a. What is the probability that a randomly selected vitamin will contain less than 82 grams of pyridoxine?
b. What is the probability that a randomly selected vitamin will contain more100 grams of pyridoxine?
c. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of
pyridoxine?
