Question no. 1:

In a group of 500 wage-earners, the weekly wages of 4% were under Rs.60 and those of 15% were under

Rs.62.50. 15% of the workers earned Rs.95 and over, and 5% of them got Rs.100 and over.

The median and quartile wages were Rs.82.25, Rs.72.75, and Rs.90.50; the fourth and sixth decile wages

were Rs.78.75 and Rs.85.25 respectively.

Put the above information in the form of a frequency distribution. Construct a Histogram and estimate

the mean wage of the 500 wage-earners therefrom.

Question no. 2

(a) : How many odd numbers between 1000 and 9999 have distinct digits?

(b) : The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12; the

probability that it is a camper is 0.28; and the probability that it is a camper with Canadian license plates

is 0.09. What is the probability that

(i) a camper entering the Luray Caverns has Canadian license plates?

(ii) a vehicle with Canadian license plates entering the Luray Caverns is a camper?

(iii) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper?

Question no. 3

(a) : The fourth mean moment of a symmetrical distribution is 243. What would be the value of the

standard deviation in order that the distribution may be mesokurtic?

(b) : In a certain distribution, the first four moments about the point 4 are -1.5, 17, -30 and 108.

Calculate b1 and b2 and state whether the distribution is leptokurtic or platykurtic?