Problem Set 3 (2)
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Drexel University *
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Course
310
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
Pages
3
Uploaded by ndk35264519
1
BMES 310 – PROBLEM SET 3 – DUE DATE: FEBRUARY 5, 2024
1.
A tire manufacturer has started a program to monitor production. In every
batch of eight tires, two will be randomly selected and electronically tested
for defects. An experiment consists of recording the condition of these two
tires: defect-free (G) or reject (B). Suppose two of the eight tires in a batch
actually contain serious defects:
a.
List the outcomes in this experiment –
GG,GB,BG, and BB.
b.
What is the probability that both tires selected will be defect free? –
6/8 * 5/7 = 15/28
c.
What is the probability that at least one of the tires selected will
contain a defect? – 1 – 15/28 =
13/28
d.
What is the probability that both tires selected will contain a defect? –
2/8 * 1/7 = 1/28
2.
According to the Census Bureau, in 2000, 86.9% of the adults in the United
States aged 65 or older were Caucasian and 8.1% were African American.
Two percent of those 65 or older are Caucasian and have had difficulty
obtaining health care and 0.3% of those 65 or older are African American and
have had difficulty obtaining health care (Source: U.S. Census Bureau, Census
2000 and Medicare Current Beneficiary Survey). Suppose an adult 65 or
older is selected at random.
a.
Suppose the adult is Caucasian, what is the probability the adult had
difficulty obtaining health care? –
0.02/0.869 = 0.023.
b.
Suppose the adult is African American, what is the probability the
adult had difficulty obtaining health care? –
0.003/0.081 = 0.037
c.
Suppose the adult is African American, what is the probability the
adult had no difficulty obtaining health care? –
1-0.037= 0.963
d.
Suppose the adult had difficulty obtaining health care, what is the
probability the adult is Caucasian? African American? –
0.02/0.02+0.003 = 0.870 and the probability the adult is African
American is 0.003/0.02+0.003 = 0.130
3.
Suppose that Saint Christopher's Hospital in Philadelphia has three
emergency generators for use in case of a power failure. Each generator
operates independently, and the manufacturer claims that the probability
each generator will function properly during a power failure is 0.95.
a.
What are the possible outcomes in case of a power failure? -
The
possible outcomes in case of a power failure are: 0 failures (FFF), 1
failure (FFT, FTF, TFF), 2 failures (FTT, TFT, TTF), 3 failures (TTT).
b. Construct the probability distribution for these outcomes letting X be the number of failures. - The probability distribution for these outcomes is:
2
BMES 310 – PROBLEM SET 3 – DUE DATE: FEBRUARY 5, 2024
X P(X) 0 0.857 1 0.135 2 0.008 3 0.000 c. Suppose a power failure occurs and all three generators fail. Is there
reason to doubt the manufacturers claim? -
Suppose a power failure
occurs and all three generators fail. The probability of this event is
0.05 ^3 =0.000125. which is very low. This suggests that there is reason
to doubt the manufacturer's claim.
4.
A new pharmaceutical agent has been developed for the treatment of certain
symptoms caused by asthma. Based on a clinical trial, the manufacturer
claims only 10% of patients at least 12 years of age using this medication will
experience tachycardia or rapid heart rate as an adverse reaction to the drug.
Suppose 30 people (at least 12 years old) who need this medication are
selected at random. Each volunteer is given the new drug and the number of
people who experience tachycardia is recorded.
A. What is the probability that at most one person will experience tachycardia? - The probability that at most one person will experience tachycardia is (
0 30
)
0.1^
0 0.9^
30
+
(
30 1 )
0.1^
1 0.9^ 29
≈0.040+0.149=0.189
b. Suppose seven people experienced tachycardia. Does this suggest that the
companies claim is incorrect? Why or why not? -
Suppose seven people experienced
tachycardia. The probability of this event is
(30 7 )0.1^7 0.9^23 ≈0.001
which is much lower than the expected probability of
0.1×30=3
This suggests that the company's claim is incorrect, or the sample is not
representative of the population.
5.
It is estimated that 14% of all drivers in Pennsylvania are uninsured.
Suppose the Pennsylvania State Police establish a checkpoint and randomly
stop cars to inspect the driver’s license, registration, and proof of insurance.
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