Statistics and Probability Answers

Explain the concept of variation and distinguish between chance cause variation and assignable cause variation.

A random sample of size 10 from a normal population gives the values,
64, 72, 65, 70, 68, 71, 65, 62, 66, 67.
If it is known that the standard error of the sample mean is √0.64 , find the 95% confidence limits for the population mean. Also find the population variance.

In order to find the correlation coefficient between two variables X and Y
from 20 pairs of observations, the following calculations were made:
Σx =15, Σy = − 6, Σxy = 50, Σx^2 = 61 and Σy^2 = 90 .
Calculate the correlation coefficient, and the slope of the regression line of Y on X.

List the merits and demerits of the mode as a measure of central tendency as compared to mean.

The police plans to enforce speed limits by using radar traps at different
locations within the city limits. The radar traps at each of the location L1 , L2 , L3 ,
and L4 , are operated 40%, 30%, 20% and 30% of the time. If a person who is
speeding on his way to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively,
of passing through these locations, what is the probability that he will receive a
speeding ticket? Also find the probability that he will receive a speeding ticket at
location L1 .

An agency wants to study some nutritional deficiency in a village.
To do that 170 boys from 8502 boys in a village showed that 21 had some nutritional deficiency.
Identify the population and parameter in this situation.
Estimate the parameter mean and standard error of the estimate.

Suppose the quantity of cream obtained from a tin of milk is uniformly distributed with a mean of 10 kg and range of 1.8 kg. Then:
i) What are the largest and the smallest amount of cream obtained from a tin of milk?
ii) What is the probability that a tin of milk will give cream weighing between 9.2 kg and 10.8 kg?

If 500 people each select a number a random between 1 and 100, what is the probability
that 4 people select the number 25?

Let two dice be thrown. What is the probability that the sum on the dice is greater than
or equal to 9?

6. The following set of data is from a sample of n=10)
7 4 9 7 12 8 10 15 7 9

a. Compute the mean, median, and mode.
b. Compute the first, second and third quartiles.
c. Compute the range, variance, standard deviation, and coefficient of variation
d. Compute the Z scores. Are there any outliers?