Question

It is known that 90% of all brand A external hard drives work in a satisfactory manner throughout the warranty period are successes"). Suppose that n - 15 drives are randomly selected. Let X - the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. (Hint: One possible value Xin is 0.2, corresponding to X - 3. What is the probability of this value (what kind of random variable is x)? (Round your answers to three decimal places.) Xin ĐX/m) 0 0 X X X X X X XSSSSSS

Answer 1

X	X/n	p(X/n)
0	0	0
1	1/15	0
2	2/15	0
3	3/15	0
4	4/15	0
5	5/15	0
6	6/15	0
7	7/15	0
8	8/15	0
9	9/15	0.002
10	10/15	0.010
11	11/15	0.043
12	12/15	0.129
13	13/15	0.267
14	14/15	0.343
15	1	0.206

The above probabilities are calculated as P(X/n) =

(15) * 0.9" * 0.115-1

m = 0 if all the three envelopes selected contain no money

Thus, P(m = 0) = = 1/120

3

m = 5 in three conditions {0 with no money, 3 with $5 or 1 with no money, 2 with $5 or 2 with no money, 1 with $5}

Thus, P(m = 5) = (3C0 * 5C3 + 3C1*5C2 + 3C2*5C1)/10C3

= 55/120 = 11/24

m = 10 in two conditions {1 with no money or $5, 2 with $10 or 2 with no money or $5, 1 with $10}

Thus, P(m = 10) = (8C1*2C2 + 8C2*2C1)/10C3 = 64/120 = 8/15

m	0	5	10
P(m)	1/120	11/24	8/15