Statistics and Probability Answers

A sample of 25 items is selected from a very large shipment. It is found to have a mean weight of 310 gm and standard deviation equal to 9 gm. State and compute the 95% confidence limits for the population mean weight.

A random sample of male employees is taken at the end of a year and the mean
number of hours of absenteeism for the year is found to be 63 hours. A similar
sample of 50 female employees has a mean of 66 hours. Could these samples be
drawn from a population with the same mean and standard deviation of 10 hours?
(Use α = 5%)

Like two situations where systematic sampling is appropriate. Justify your choice
of situations. Also explain how it is different from stratified sampling. Justify

Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the
probability that exactly 2 of 8 industrial accidents will be due to fatigue.

The mean salary paid to 500 employees working in a firm was found to be Rs. 180.40. After disbursement of salaries for a certain month, it was discovered that the salary of two employees was wrongly entered as Rs. 297 and Rs. 165 against their correct salary of Rs. 197 and Rs. 185, respectively. Find the correct mean salary.

The regression equation of y on x and that of x on y are 8x-10y+66=0 and 40x-18 y = 214 respec tively, and the variance of x is 9.
i) What are the mean values of x and y?
ii) Find σy.
iii) Find the coefficient of correlation between x and y.

The 15 stocks had the following percentage changes in value over the past year:
3 0. 6 -5 -2
5 -18 20 14 18
-10 10 50 -20 18
Compute the range, median, 20th percentile, inter-quartile range.

Consider a random variable X having the uniform density function f ( x ) with a = 20 and b= 30
i) Define and graph the density function f(x).
ii) Verify that f(x) is a probability density function.
iii) Find P(22≤x≤30). iv) Find p( x= 25)

If the second moment of a Poisson distribution is 6, find the probability p ( x≥ 2)

Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads a marble is chosen from Box I, if it turns up tails a marble is chosen from Box II. Find the probability that a red marble is chosen.

Find the variance and the standard deviation of the sum obtained in tossing a pair of fair dice.

A bank wishing to determine the average amount of time a customer must wait to be served took a random sample of 100 customers and found that the mean waiting time was 2.7 minutes. Assuming that the population standard deviation is known to be 15 minutes, find the %90 confidence interval estimate of the mean waiting time for all the bank’s customers.