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The average marks in the mathematics of a sample of 100 students was 51 with a S.D. of 6 marks .Could this have been a random sample from the population with average marks 50.
The joint pdf of random variables ‘X’ and ‘Y’ is
fx,y=12, 0<x<y, 0<y<2
Find
a. The marginal pdfs, fX(x) and fY(y).
b. The conditional pdfs, fX/Y(x/y) and fY/X(y/x)
c. The E(X/Y=1)
d. Are ‘X’ and ‘Y’ statistically independent?
In a city, it is estimated that the maximum temperature in June is
normally distributed with a mean of 23o
and a standard deviation of 5
o
.
Calculate the number of days in this month in which it is expected to
reach a maximum of between 21° and 27°.
Household size in the United States has a mean of 2.6 people and standard deviation of 1.4 people. It should be clear that this distribution is skewed right as the smallest possible value is a household of 1 person but the largest households can be very large indeed.
(a) What is the probability that a randomly chosen household has more than 3 people?
A normal approximation should not be used here, because the distribution of household sizes would be considerably skewed to the right. We do not have enough information to solve this problem.
(b) What is the probability that the mean size of a random sample of 10 households is more than 3?
By anyone’s standards, 10 is a small sample size. The Central Limit Theorem does not guarantee sample mean coming from a skewed population to be approximately normal unless the sample size is large.
(c) What is the probability that the mean size of a random sample of 100 households is more than 3?
Which is shorter, a 95% z-interval for the mean or a 95% t-interval for the mean? Is one of these always shorter, or does the outcome depend on the sample
Find the area under the standard normal curve than z=0.5
Will scored 625 on the SAT math portion. The math portion of the SAT has an average of 508 and a standard deviation of 110. Stephanie scored 25 on her ACT math portion. The math portion of the ACT has an average of 21 and a standard deviation of 4.7. Find the z- score for each student. Which statement below describes the student that has the more impressive score and why?
assume that the salaries of the elementary school teachers in the united states are normally distributed with a mean of $31,450 and a standard deviation of $2,995. What is the cutoff salary for teachers in the bottom 15%?
Student Height (x) 1.47 Hazel Kim Mee Ann Mae 1.58 Grace Ann 1.67 Jethro 1.69 1.51 Chelsea Mae TOTAL 7.92 STEPS: 1. Solve for the mean of the population u. 2. Solve for the mean of the sampling distribution of the sample means 3. Compare p and 4. Solve for the variance (0 ?) and the standard deviation (a) of the population. 5. Solve the variance (0 x) and the standard deviation (ox) of the sampling distribution of the sample means 6. Compare o and on
the sample mean is computed from a random sample of size 25 drama from a population having SD find i)90% ii) 99% confidence interval of the population mean
