IE121-OLA3 3rdQ 1516 answers

IE121 – OLA 3
3rdQ 2015 – 2016
OLA3 Stat1 Answer Key
Binomial b(x; n, p) = nC x x (P) x x (1-P) n-x
Hypergeometric h(x; N, n, k) = [ kC x ] [ N-kC n-x ] / [ NC n ]
Poisson P(; x) = (e -μ ) (μ x ) / x!
1. Suppose that a shipment contains 5 defective items and 10 non defective items. If 7 items are
selected at random without replacement, what is the probability that at least 3 defective items will
be obtained? (10pts)
ANS: h(x; N, n, k) = h(x2) = 1 – P(0) + P(1) + P(2) = 1-0.5734 = 0.4266
2. The mean number of cracks in South Super Highway that needs repair is 2 cracks per kilometer.
a. What is the probability there are at most 4 cracks that requires repair for every 3 kilometers?
b. What is the probability that at least one crack requires repair in 2 kilometers of highway? (5pts)
ANS:
a. P(; x) = (e -μ ) (μ x ) / x!
P(6; x=4) = 1 - (e -4 ) (4 0 ) / 0! = 0.9817
3. If the probability that a regular LED bulb has a useful life of at least 1,000 hours is 0.9, find the
probabilities that among 20 such lights
a. at least 15 will have a useful life of at least 1000 hours. (5pts)
b. at least 2 will not have a useful life of at least 1000 hours. (5pts)
ANS: a. b(x>=15; 20, 0.9) = 0.9888
b. b(x>=2; 20, 0.9) = 1 – 0.3917 =0.6083
4. An acceptance plan calls for the inspection of a sample of 75 articles out of a lot of 1500. If there
are no nonconforming articles in the sample, the lot is accepted; otherwise, it is rejected.
a. Find the probability that if a lot of 1% nonconforming is submitted, it will be accepted. (10pts)
b. If a lot containing 2% nonconforming is inspected, what is the probability that it will be
rejected? (20pts)
ANS: Binomial b(x; n, p) = nCx x (P) x x (1-P) n-x
a. b(0, 75, 0.01) = 0.4706
b. b(0, 75, 0.02) = 0.2198 accepted
b(0, 75, 0.02) = 1-0.2198 = 0.7082 rejected
5. Nokia usually placed their phones in a functional test after being populated with semiconductor
chips. 1 batch contains 3000 cellphones, and 20 are selected without replacement for functional
testing.

a. What is the probability that at most 1 defective cellphone is in the sample if 30 cards are
defective? (10pts)
b. What is the probability that at least 1 defective cellphone appears in the sample if 90 cards are
defective? (10pts)
ANS: a. h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]
h(x≤1; 3000, 20, 30) = [ 30C0 ] [ 3000-30C20-0 ] / [ 3000C20 ] + [ 30C1 ] [ 3000-30C20-1 ] / [ 3000C20 ]
h(x≤1; 3000, 20, 30) = 0.8174 + 0.1662 = 0.9836
b. h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]
h(x≥1; 3000, 20, 90) = 1 – [ 90C0 ] [ 3000-90C20-0 ] / [ 3000C90 ]
h(x≥1; 3000, 20, 90) = 1 – 0.5427 = 0.4573
6. Mars Inc. claims that 20% of its M&M plain candies are blue, and a sample of 100 such candies is
randomly selected.
a. Find the mean and standard deviation for the number of blue candies in such sample of 100.
(5pts)
b. From range rule of thumb, any result is considered unusual if it differs by more than two
standard deviation from the mean. If a sample of 100 M&M plain candies only has 5 blue
candies, is this result unusual? Does it seem that the claim rate of 20% is wrong? (5pts)
a. Mean μ = np = 100 (0.20) = 20.0
Standard deviation σ = =
= 4
b. Using range rule of thumb, the unusual values are
< μ – 2σ = 20.0 – 2(4.0) = 12
Or > μ + 2σ = 20.0 + 2(4.0) = 28
** It is unusual for the pack of M&M candies to have blue candies lower than 12.
npq
100(0.20) (0.80)
5. Suppose on the average, 1 out of 20 students cannot answer this question correctly. If 40 of this
kind of question are selected at random and checked, find the probability that
a. 4,5 or 6 questions will be answered incorrectly.
b. more than 2 questions will be answered incorrectly.
ANS: p = 1/20 n = 40 = 1/20 (40) = 2
a. P(2; 4