Normal Distribution
NORMAL DISTRIBUTION
1. Find the distribution: a.
b.
c.
d.
e.
f.
following probabilities, the random variable Z has standard normal
P (0< Z < 1.43)
P (0.11 < Z < 1.98)
P (-0.39 < Z < 1.22)
P (Z < 0.92)
P (Z > -1.78)
P (Z < -2.08)
2. Determine the areas under the standard normal curve between –z and +z:
♦ z = 0.5
♦ z = 2.0
Find the two values of z in standard normal distribution so that:
P(-z < Z < +z) = 0.84
3. At a university, the average height of 500 students of a course is 1.70 m; the standard deviation is 0.05 m. Find the probability that the height of a randomly selected student is:
1. Below 1.75 m
2. Between 1.68 m and 1.78 m
3. Above 1.60 m
4. Below 1.65m
5. Above 1.8 m
4. Suppose that IQ index follows the normal distribution with µ = 100 and the standard deviation σ = 16. Miss. Chi has the IQ index of 120. Find the percentage of people who have the IQ index below that of Miss. Chi.
5. The length of steel beams made by the Smokers City Steel Company is normally distributed with µ = 25.1 feet and σ = 0.25 feet.
a. What is the probability that a steel beam will be less than 24.8 feet long?
b. What is the probability that a steel beam will be more than 25.25 feet long? c. What is the probability that a steel beam will be between 24.9 and 25.7 feet long?
d. What is the probability that a steel beam will be between 24.6 and 24.9 feet long?
e. For a particular application, any beam less than 25 feet long must be scrapped. What is the probability that a beam will have to be scrapped?
6. The daily trading volumes (millions of shares) for stocks traded on the New York
Stock Exchange for 12 days in August and September are shown here (Barron’s,
August 7, 2000, Sep. 4, 2000, and Sep. 11, 2000).
917
983 1046
944
723 783
813
1057 766
836
992 973
The probability distribution of trading volume is approximately normal.
a. Compute the mean and standard deviation for the daily trading volume to use as estimates of the population mean and standard deviation.
b. What is the
1. Find the distribution: a.
b.
c.
d.
e.
f.
following probabilities, the random variable Z has standard normal
P (0< Z < 1.43)
P (0.11 < Z < 1.98)
P (-0.39 < Z < 1.22)
P (Z < 0.92)
P (Z > -1.78)
P (Z < -2.08)
2. Determine the areas under the standard normal curve between –z and +z:
♦ z = 0.5
♦ z = 2.0
Find the two values of z in standard normal distribution so that:
P(-z < Z < +z) = 0.84
3. At a university, the average height of 500 students of a course is 1.70 m; the standard deviation is 0.05 m. Find the probability that the height of a randomly selected student is:
1. Below 1.75 m
2. Between 1.68 m and 1.78 m
3. Above 1.60 m
4. Below 1.65m
5. Above 1.8 m
4. Suppose that IQ index follows the normal distribution with µ = 100 and the standard deviation σ = 16. Miss. Chi has the IQ index of 120. Find the percentage of people who have the IQ index below that of Miss. Chi.
5. The length of steel beams made by the Smokers City Steel Company is normally distributed with µ = 25.1 feet and σ = 0.25 feet.
a. What is the probability that a steel beam will be less than 24.8 feet long?
b. What is the probability that a steel beam will be more than 25.25 feet long? c. What is the probability that a steel beam will be between 24.9 and 25.7 feet long?
d. What is the probability that a steel beam will be between 24.6 and 24.9 feet long?
e. For a particular application, any beam less than 25 feet long must be scrapped. What is the probability that a beam will have to be scrapped?
6. The daily trading volumes (millions of shares) for stocks traded on the New York
Stock Exchange for 12 days in August and September are shown here (Barron’s,
August 7, 2000, Sep. 4, 2000, and Sep. 11, 2000).
917
983 1046
944
723 783
813
1057 766
836
992 973
The probability distribution of trading volume is approximately normal.
a. Compute the mean and standard deviation for the daily trading volume to use as estimates of the population mean and standard deviation.
b. What is the