Question

3. A store owner receives a large shipment of shirts of various colors. The shipment has approximately 55% blue shirts. The store owner randomly selects eight shirts to put on display. The number of blue shirts among those selected for display is denoted by the binomial random variable X. Parameters are n = 8 and p = 0.55. (a) [10 points] Create the binomial probability distribution table for X (values) showing columns for X , P(X), and X*P(X). Sum the P(X) and X*P(X) columns. (b) [10 points] Make the histogram of the distribution with X on the horizontal axis and P(X) on the vertical axis. (c) [10 points] Write the formulas and values for the probability that exactly five blue shirts are selected and the probability that less than five blue shirts are selected.

Please show probability distribution table and histogram below

Answer 1

#Given:

n=8

p=0.55

Ansa:

x~Binomial(n=8,p=.55)

x=0,1,--n

=0 ow

x	P(x)	x*P(x)
0	0.001682	0
1	0.016441	0.016441
2	0.070333	0.140666
3	0.171925	0.515775
4	0.262663	1.050652
5	0.256826	1.28413
6	0.156949	0.941695
7	0.054808	0.383654
8	0.008373	0.066987
Sum	1	4.4

Ansb:

histogram  

Ansc:

P(x=5)

#probability that less than five blue shirts are selected. is 0.5230