The proportion of male and female students .in a class is found to be 2. What is the probability that out of 4 students selected at random with replacement

2 or more will be females

no male student is selected

50 students selected at random from 500 students enrolled in a computer crash programme were classified according to the age and grade points giving the following data:

Age in Years
Grade Points Below 20 21-30 Above 30

upto 5 3 5 2
5.1-7.5 8 7 5
7.6 10.0 4 8 8

Test at level of significance that age and grade points are independent. (You may like to use the values given at the end of the question paper.)

Packets of certain washing powder are filled with an automatic machine. If the weights of the packets are normally distributed with an average weight of 5 kg and a standard deviation of 50 gm, find the percentage of the packets having weight above 5.10 kg.

A steel rod is subjected to stress. The tensile strength of the rod at different values of the stress are recorded. Find a relation between the tensile strength and the stress. The data is given below

Stress 10 9 7 8 11
Tensile strength 6 3 2 4 5

Predict the tensile strength at a stress of 5 kg.

An executive makes on an average 5 telephone calls per hour at a cost which may be taken as 2 per call. Determine the probability that in any hour, the cost of the telephone calls

exceeds RS

remains less than RS 10.

In a watch factory, watch cases are manufactured and the production for ten years is given below. Determine the trend values by using a 3-year moving average.

Year Production (in 1000 tonnes)
2001 26
2002 27
2003 28
2004 30
2005 29
2006 27
2007 30
2008 31
2009 32
2010 31

Plot the values and interpret.

Which statistics is a point estimate of variance when the random sampling follows normal distribution? Justify.

Let a population of 200 units be divided into 4 strata of size N1 N2 N3 N4 50 and let the corresponding sample sizes allocation to these 4 stratas be n1 n2 n3 n4 respectively. Also let the value of Yhi of study variable for the ith unit in the hth stratum h be given by Yhi. h for all i. Calculate the value of the terms yh S^2h and The symbols used here have their usual meanings.

A company wants to test whether its salesmen Band C have the same selling ability. Their records of sales (in RS 1000) during various months are given below:

Salesmen April May June

A 16 21 18
B 22 20 15
C 25 24 16

Prepare an ANOVA table and test the hypothesis that the mean sales per month of all the salesmen are equal at level of significance. (You may like to use the values given at the end of the question paper.)

The following table gives the number of car accidents in Delhi that occurred during various days of the week:

Day Number of accidents
Day 1 14
Day 2 16
Day 3 8
Day 4 12
Day 5 11
Day 6 9
Day 7 14

Test at level of significance whether the accidents are uniformly distributed over the days of the week. (You may like to use the values given at the end of the question paper.)

Suppose from a total of 120 guava bearing trees in a village, 5 clusters of 4 trees each are selected and yield (in kg) recorded is as given in the following table

Cluster Number Yield (in kg)
Tree 1 Tree 2 Tree 3 Tree 4
1 2 22 8 6
2 26 10 19 11
3 4 4 2 15
4 10 2 4 7
5 9 15 10 10

Estimate the average yield (in kg) per tree of guava using cluster sampling method and simple random sampling method.

Of the 200 people selected randomly from a large city, 120 were found to be in favour ofa more liberal divorce law. Obtain a 95% confidence interval of the proportion of the people in the city who favour more liberal divorce laws.

The number of defects in items are given as

Find the suitable control limits and plot the graph and interpret it.

A sample of size 3 is to be selected from a population of 10 households. List all the possible samples by

Linear Systematic Sampling

Circular Systematic Sampling Also compare the two.

7. Find which of the following statements are True and which are False by giving justification.

Sampling distribution and Standard error are same.

If the sample follows normal distribution, N then Y is the point estimate for M.

The number of six-digit telephone numbers generated with distinct digits is 96.

Control limits in control charts are based on normal distribution.

For a uniform distribution 0 x =1.