Question

(1) Given the distribution

                                          

x	11	24	3	4
p(x)	.4	.3	.2	.1

.

check if this distribution is a probability distribution.

If it is, find the mean and the standard deviation.

2) Given the following sample 2, 3, 8, 3, 4

      find the mean, median, mode and standard deviation

  3) The investment company has 4 different bonds ( P, Q, R and S ). In each bond they have number of shares shown in the chart

      

Bond          P              Q              R               S

Shares         24             2              12              14

If they want to sell one share randomly, what is the probability that they will sell a share from bond Q?

   4) To find out how uniformly babies grow, we measured the weights of random eight babies first at 11 months and then at 27 months. We obtained the following data.

Weight at 11 months             Weight at 27 months

         14                                           25                                   

         14                                           28

         20                                           26

         17                                           24

         15                                           22

         17                                           27

         15                                           23

         16                                           25

Evaluate the correlation coefficient and describe the correlation.

(5) There are 2 orange, 4 green, 3 blue and 2 black balls in a bag. You take    4 balls, one by one, with replacement, randomly from the bag. What is the probability that you will get exactly two green balls? How many green balls do you expect to get?

Answer 1

1) Mean = 0.4*11+0.3*24+0.2*3+0.1*4 = 12.6

Variance = 0.4*11*11+0.3*24*24+0.2*3*3+0.1*4*4 -12.6*12.6 =65.84

Standard deviation = $\sqrt{65.84}$

= 8.11