Question

The best-selling basketball sneaker of all time is the converse 8220 chuck taylor 8221 all star. suppose chuck taylor 8221's are sold in holabird sports and are available in sizes from 7 to 13. the size purchased is a random variable with probability distribution given in the table below.

x - 7, 8, 9,10,11,12,13

p(x) - 0.05, 0.08, 0.10, 0.14, 0.28, 0.21, 0.14

a. find the mean, variable, and standard deviation of the sneaker size purchased.

b. find the probability that a random selected customer buys a pair of these sneakers with size greater than one standard deviation to the right of the mean.

c. suppose three randomly selected customers each purchase a pair of these sneakers. what is the probability that exactly two of the three buy size 11 sneakers?

Answer 1

a)

X	P(X)	X*P(X)	X² * P(X)
7	0.05	0.35	2.45
8	0.08	0.64	5.12
9	0.10	0.90	8.10
10	0.14	1.40	14.00
11	0.28	3.08	33.88
12	0.21	2.52	30.24
13	0.14	1.82	23.66

	P(X)	X*P(X)	X² * P(X)
total sum =	1	10.71	117.45

mean = E[X] = Σx*P(X) =            10.7100
          
E [ X² ] = ΣX² * P(X) =            117.4500
          
variance = E[ X² ] - (E[ X ])² =            2.7459
          
std dev = √(variance) =            1.6571

b)

P(X>µ+σ) = P(X>12.37)=P(X=13) = 0.14

c)

n=3

p=0.28

P ( X =    2   ) = C(3,2) * 0.28^2 * (1-0.28)^1 =            0.1693