What is the probability of mission success if there are 16 trucks scheduled for a 20-hour mission and at least 10 trucks must operate for the entire duration of the mission if each truck has a failure rate of 1 failure per 100 hours?
In: Statistics and Probability
Draw a probability tree diagram for the following experiment: Suppose there are five balls in an urn. Three are red and two are blue. We will select a ball, note the color, and, without replacing the first ball, select a second ball. What is the sample space of this
experiment? What is the associated probability distribution in this
experiment?
In: Statistics and Probability
Use the Central Limit Theorem to calculate the following
probability. Assume that the distribution of the population data is
normally distributed. A person with “normal” blood pressure has a
diastolic measurement of 75 mmHg, and a standard deviation of 4.5
mmHg.
i) What is the probability that a person with “normal” blood
pressure will get a diastolic result of over 80 mmHg, indicating
the possibility of pre-hypertension?
ii) If a patient takes their blood pressure every day for 10 days, what is the probability of getting an average diastolic blood pressure result of over 80 mmHg, assuming the patient has normal blood pressure.
iii) What can we conclude about such a result (based on preceding calculation)?
In: Statistics and Probability
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is
0.267
Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a)
What is the probability that among
18
randomly observed individuals exactly
4
do not cover their mouth when sneezing?
(b)
What is the probability that among
18
randomly observed individuals fewer than
6
do not cover their mouth when sneezing?
(c)
Would you be surprised if, after observing 18
individuals, fewer than half covered their mouth when sneezing? Why?
In: Statistics and Probability
According to a study done by a university student, the
probability a randomly selected individual will not cover his or
her mouth when sneezing is 0.267. Suppose you sit on a bench in a
mall and observe people's habits as they sneeze.
(a) What is the probability that among 16 randomly observed
individuals exactly 5 do not cover their mouth when
sneezing?
(b) What is the probability that among 16 randomly observed
individuals fewer than 6 do not cover their mouth when
sneezing?
(c) Would you be surprised if, after observing 16 individuals,
fewer than half covered their mouth when sneezing? Why?
In: Statistics and Probability
For an acceptance sampling plan with
n = 25 and c = 0,
find the probability of accepting a lot that has a defect rate of 4%. (Round your answer to four decimal places.)
What is the probability of accepting the lot if the defect rate is 8%? (Round your answer to four decimal places.)
In: Statistics and Probability
7. A genetic disorder occurs with probability 1/2000 . There is a test for this genetic disorder. If you have the disorder, then you test positive 90% of the time. If you don’t have the disorder, then you test negative 90% of the time.
If you test positive, what is the probability that you have the disorder?
In: Statistics and Probability
In one city, the probability that a person will pass his or her driving test on the first attempt is 0.7. Assume that 10 people are selected at random from among those taking their driving test for the first time.
(a) [5 points] What are the values of n, p, and q in this problem?
(b) [30 points] What is the probability that at least 8 of the 10 selected people pass the test?
(c) [10 points] Determine the mean and variance of the binomial random variable corresponding to this problem.
In: Statistics and Probability
For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts (a) through (c) below. x (cash prize, $) P(x) 14,000,000 0.00000000547 200,000 0.00000032 10,000 0.000001604 100 0.000165836 7 0.004321645 4 0.008019353 3 0.01545068 0 0.97204055653 If the grand prize is $14,000,000, find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket?
x (cash prize, $) P(x)
14,000,000 0.00000000547
200,000 0.00000032
10,000 0.000001604
100 0.000165836
7 0.004321645
4 0.008019353
3 0.01545068
0 0.97204055653
If the grand prize is
$14,000,000,
find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket?
In: Statistics and Probability
Of all the trees planted by a landscaping firm, 75% survive.
What is the probability that 11 or more of the 13 trees they just
planted will survive? (Use a table of binomial probabilities. Give
your answer correct to four decimal places.)
In: Statistics and Probability