Statistics and Probability Answers

4. a) Plating of gold on wrist watches requires a chemical called . AiCI 3

Concentration of

the chemical that is added to the solution is an important factor. The objective is to

choose that concentration for which plating is uniform. Three concentration of AiCI 3

chosen were 5%, 15% and 20%. These were added in the solution and plating was

done and thickness (in units) measured on 5 samples is gives below.

Sample

→

↓

Conc. of AiCI3

1 2 3 4 5

5% 3 2 4 2 4

15% 4 4 3 2 4

25% 3 3 4 4 2

Use ANOVA to comment on whether the concentration of AiCI gives same result or 3

not. (Use 05.0 α = )

3b) In a locality of 18,000 families, a random sample of 840 families was taken. Of these

840 families, 206 families were found to have a monthly income of Rs. 500 or less.

Give the confidence interval for the families having income Rs. 500 or less.

3. a) Two samples of 9 and 8 sizes give the sum of squares of deviations from respective

means equal to 160 and 91 inches squares. Test whether these samples have been

drawn from same normal population or not? (Use 05.0 α = )

2b) A bicycle shop sells the following number of bicycles from 1990 to 2000.

Year Number sold

(thousands)

1990 3

1991 3

1992 3

1993 3

1994 6

1995 6

1996 6

1997 6

1998 9

1999 10

2000 12

Compute the first three moving averages of length 3 for the bicycle sales data and

place them in line with the corresponding year.

2. a) There are two samples of 1200 and 900 people drawn from populations respectively,

which have 30% and 25% of fair-haired people. Test whether the samples drawn

from this population maintain difference or not. (Use α = 05.0 )

1b) Two cards are drawn simultaneously or successively without replacement from a

well-shuffled deck of 52 cards. Find the probability distribution of number of aces

).x( Give a graphical representation of probability distribution

1. a) Following is the distribution of marks (out of 25) obtained by 10 students in Physics

and Mathematics.

No. Physics

(X )i

Mathematics

(Y )i

2 Xi

2 Yi

XiYi

1 18 21 324 441 378

2 20 23 400 529 460

3 11 14 121 196 154

4 20 23 400 529 460

5 14 17 196 289 238

6 15 18 225 324 270

7 13 16 169 256 208

8 16 19 256 361 304

9 17 20 289 400 480

10 20 23 400 529 460

Total 164 194 2780 3854 3412

Draw a scatter diagram for all the 10 students and calculate the correlation between

marks of Physics and Mathematics.

6(b) Based on the previous data, the probabilities of a batsman making various scores in

One Day Internationals are given below: (5)

Runs 10 20 30 50 60 70 100

Probability 0.01 0.20 0.15 0.30 0.12 0.2 0.02

Simulate the runs scored by the batsman in the next five One Day Internationals using

the following 25, 39, 65, 76, 12.

9(b) Suppose the quarterly sales for a particular make of a car in Delhi were 2682, 2462

and 3012, respectively. From the past data prior to these three data points, a straight

line was to fit. The value on the line corresponding to the last observed time is 2988

and the slope is 80. Use exponential smoothing based upon the three observations

given above to forecast sales for the quarterly period following these observations,

using α = β = 0 ⋅ .2 (4)

8(b) The mean arrival rate to a service centre is 3 per hour. The mean service time is found

to be 10 minutes foe service. Assuming Poisson arrival and exponential service time,

find (4)

(i) the utilisation factor for this service facility,

(ii) the probability of two units in the system,

(iii) the expected number of units in the system, and

(iv) the expected time in hours that a customer has to spend in the system.