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In a study of perception, 80 men are tested and 7 are found to have red/green color blindness. What sample size would be needed to estimate the proportion of male red/green color blindness if we wanted 96% confidence that the sample proportion is in error by no more than 0.03?
A university administrator would like to estimate the true mean salary of all professors at the university. She uses $4000 as the population standard deviation of the salary of all professors at the university. What sample size would be required so that a 90% confidence interval for 𝜇 has a length of $2000?
P(X = x) = {
1
3
x, if x ∈ {1,2}
0, otherwise.
The weights of packages filled by machine are normally distributed about a mean of 25 ounces, with a standard deviation of one ounce. What is the probability that n packages from the machine will have an average weight of less than 24 ounces if n = 1, 4, 16, 64? (10)
A magic bag contains of 10 good articles, 4 with minor defects and 2 with major
defects. Two articles are chosen from the magic bag at random. Find the
probability [5]
(a) Exactly 1 is good
(b) Neither is good
(c) Both has major defects
If random variable (x) takes vales 1, 2, 3, 4 such
that 2 P(x=1) = 3 P (x=2) = P(x=3) = 5 P (x=4)
Find the probability distribution function (PDF) and cumulative distribution function
(CDF), also state the properties of PDF and CDF.
Consider all samples of size 5 from this population.
2,5,6,8,10,12,13
1. Compute the mean and the standard deviation of the population.
2. List all samples of size 5 and compute the mean for each sample.
3. Construct the sampling distribution of the sample means.
4. Calculate the mean of the sampling distribution of the sample means.
Compare this to mean of the population.
5. Calculate the standard deviation of the sampling distribution of the
sample means . Compare this to the standard deviation of the
population.
If X and Y are independent random variables each following N(0, 2), find the pdf of Z = 2X + 3Y .
MD=SD=R/2 (Sign are natural)
