Assignment about Math 125009 (STATISTICS).

Math *125*009 (STATISTICS)
MUST SHOW ALL WORK
1. A manufacturing machine has a 2% defect rate.
If 3 items are chosen at random, what is the probability that at least one
will have a defect?
let P be the probability of defective item and
p=0.02
q=1-0.02 = 0.98
P(at least 1defective)= 1 – P(Non-defective)
P( Non-defective) = 0.983
P(at least 1defective)= 1 – 0.983 = 0.0588
2. A high School baseball player has a 0.287 batting average. In one game,
he gets 9 at bats. What is the probability he will get at least 5 hits in the
game?
P= 0.287
P(x)=(n
x )Px (1−P)n−x
P(x=5) = (9
5 )0.2875 (1−0.287)9−5
= 0.0634
P(x=6)= (9
6 )0.2876 (1−0.287)9−6
= 0.0170
P(x=7)= (9
7 )0.2877 (1−0.287)9−7
= 0.00293
P(x=8)= (9
8 )0.2878 (1−0.287)9−8
= 0.00029
P(x=9)= (9
9 )0.2879 (1−0.287)9−9
= 0.00001
P( atleast 5 hits) = 0.0634+0.0170+0.00293+0.00029+0.00001
=0.08363