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Estimate the true mean GPA with 99% confidence.
- In a learning style study, 1200 respondents were asked if they can assimilate concepts while watching television. 568 said Yes. Find a 95% confidence interval for the population p (Explain your solutions):
a. What is α?
b. What are the confidence coefficients?
c. what are p and q?
d. The error E is approximately?
e. What are the lower and upper limits?
f. The true population proportion falls between?
(1) Let the joint distribution function of X1 and X2 be given by
f(x1, x2) = {
8x1x2, 0 < x1 < x2 < 1
0, elsewhere
find (i) E[X2|X1] (ii) Var[X2|X1]
Estimate the true mean GPA with 99% confidence.
- In a gymnasium, a physical exercise has a mean length of 30 minutes with a standard deviation of 6 minutes. A PE major wants to estimate the true mean length of the exercise with maximum error pegged at 0.5 adopting the 95% confidence interval. How many respondents does he need? Explain how you arrived at your answer.
Consider all samples of size 5 from this population: 2 5 6 8 10 12 13
a) Compute the mean (μ) and standard deviation (σ) of the population.
b) Calculate the mean and the standard deviation of the sampling distribution of the sample means.
A random variable X is normally distributed with a mean of 45 and standard deviation of 3.If the area to the right of Z is 0.9292, what will be the value of its random variable X
A random variable X is normally distributed with a mean of 45 and standard deviation of 3. What is the value of the random variable X if the area to the left of Z is 0.1255
The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine standard deviation
How many samples of size n=3 can be selected from a population with the following sizes: N=4, N=8, N=20, N=50? A population consists of the five numbers 2, 3, 6, 8 and 11. Consider samples of size 2 that can be drawn from this population.
Two students are to be selected at random from a class with 10 girls and 12 boys. What is the probability that both will be girls, if selected
a) With replacement
b) Without replacement
A student has 6 different notebooks and decided to give 5 of them to a friend. How many ways does he have to give away these notebooks?
