Question

10. Let x be the number of PC computers are repaired at the Best Buy in Green Acres Mall on a randomly selected day. This data is represented in the discrete probably distribution table below

(x)	1	2	3	4	5
P(x)	0.16	0.22	?	0.20	0.14

1. Find the probability that 3 computers were repaired that day.
2. Find the mean of this probability distribution
3. Find the standard deviation of this probability distribution
4. Find probability that at most 4 computers were repaired.

Answer 1

a)

Sum of probabilities equal to 1

P(X) = 1

0.16 + 0.22 + P(X = 3) + 0.20 + 0.14 = 1

0.72 + P (X = 3) = 1

P (X = 3) = 0.28

b)

Mean = x * P(X)

= 1 * 0.16 + 2 * 0.22 + 3 * 0.28 + 4 * 0.20 + 5 * 0.14

= 2.94

c)

Standard deviation = Sqrt [ x² * P(X) - mean² ]

= sqrt [ 1² * 0.16 + 2² * 0.22 + 3² * 0.28 + 4² * 0.20 + 5² * 0.14 - 2.94² ]

= 1.2714

d)

P( X <= 4) = 1 - P(X = 5)

= 1 - 0.14

= 0.86