Q1: [3+3+4 Marks] The below table gives the blood plasma endorphin concentration of eleven runners before and after completing the Great North run successfully. There is a marked difference between these concentrations.

(Difference =After Before)

Before	After	DIFFERENCE
4.3	29.6	25.3
4.6	25.1	20.5
5.2	15.5	10.3
5.2	29.6	24.4
6.6	24.1	17.5
7.2	37.8	30.6
8.4	20.2	11.8
9.0	21.9	12.9
10.4	14.2	3.8
14.0	34.6	20.6
17.8	46.2	28.4

1. Calculate the sample mean, and the sample median of the difference between after and before.

Answer:

Count: 11

Sum: 206.1

Mean: 18.736363636364

Median: 20.5

1. Compute the range and the inter-quartile range for the difference;

Lowest value: 3.8

Highest value: 30.6

Range: 26.8

Lower quartile (xL): 11.8

Upper quartile (xU): 25.3

Interquartile range (xU-xL): 13.5

1. Calculate the standard deviation for the difference;

Standard deviation (): 7.9420941510493

Q-2: [ 3+5+2Marks]

1. How many positive integers less than 100 can be written using the digits 6, 7, 8 and 9?( repetition is not allowed)

Number of sample points in set ( n ) = 4

Number of sample points in each permutation ( r ) = 2

Number of permutations (n things taken r at a time) = 12

1. How many license plates of 3 symbols (letters and digits) can be made using at least one letter in each? ( repetition is allowed)

26 * 36 * 36 = 33,696

1. How many even 2-digit whole numbers less than 50 are there using the digits 1-9?

20

Q-3: [3+3+2+2 Marks] The Gift Basket Store had the following premade gift baskets containing the following combinations in stock.

	Cookies	Mugs	Candy	TOTAL
Coffee	20	13	10	43
Tea	12	10	12	34
TOTAL	32	23	22	77

Choose one basket at random. Find the probability that it contains

1. Coffee or candy;

20/77 + 13/77 + 10/77 + 10/77 + 12/77 - 10/77 = 5/7 = 0.7142857143

1. Tea given that it contains mugs;

10/23

1. Coffee given that it contains cookies;

20/32

1. Tea and cookies.

12/77

Q-4: [2+3+3+2 Marks] In an experiment, two fair dice with faces numbered, 1 through 6, are tossed and the sum =x+y, is recorded at each toss.

1. Find the sample space.

2. Let the random variable S be the sum that is recorded at each toss, find the probability distribution (mass function) of the random variable S.

3. Find the cumulative distribution function of the random variable S and use it to compute P (6s 11).

4. Calculate the expected value for the sum in this experiment.

Q-5: [4+2+4 Marks] Five coins are tossed. Let the random variable X be the number of heads. The cumulative distribution is given by the following table:

X	0	1	2	3	4	5
F(x)	1/32	6/32	16/32	26/32	31/32	1

1. Find the probability distribution of the random variable X. find P(X<5), and P(X > 3).

2. Find the expected value of the random variable X.

3. Find the standard deviation of the random variable X.

Q-6: [4+6 Marks] The interval between two successive vehicles passing a point on K winana Freeway is a probability density function. The cumulative distribution of this function is given by:

F (t) =( 40t- t)/400, 0 t 20

1. Find the density function.

b) Find the probability that the intervals between successive vehicles are:

i) At most 10 seconds;

ii) More than 5 seconds;

ii) Between 5 and 10 seconds.

PLEASE CHECK AND HELP ANSWER THE REST