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King Abdulaziz University
Faculty of Science
Department of Statistics
Assignment (2)
First Semester (1435-1436H)
Stat 271
Answer the following questions
Ex. (1) Compute the mean and the variance of the following discrete probability
distributions.
a)
x
0
1
2
3
P(x)
0.2
0.4
0.3
0.1
x
2
8
10
P(x)
0.5
0.3
0.2
b)
Ex. (2) The mean of a normal probability distribution is 500. The standard deviation
is 10.
a) About 68% of the observations lie between what two values?
b) Practically all of the observations lie between what two values?
c) About what percent of the observations lie between 400 and 550?
Ex. (3) A population consists of the following four values: 12, 12, 14, and 16.
a) List all samples of size 2, and compute the mean of each sample.
b) Compute the maen of the distribution of the sample mean and the population
mean.
c) Compute the dispression in the population with that of the sample mean/
Ex. (4) A normal population has a mean of 75 and a standard deviation of 5. You
select a sample of 40. Compute the probability the sample mean is;
a)
b)
c)
d)
Less than 74.
Between 74 and 76.
Between 76 and 77.
Greater than 77.
Ex. (5) A normal population has a mean of 60 and a standard deviation of 12. You
select a sample of 9. Compute the probability the sample mean is;
a) Greater than 63.
b) Less than 56.
c) Between 56 and 63.