Chris had heard god things about pilot fountain pens writing well right out of the box. he decides to test this by buying pilot pens until he gets one that does not write well. assume 95% of pilot pens write well right out of the box.
a. how many pens do you expect Chris to buy?
b. what is standard deviation of the number of pens Chris buy?
c. . what is standard deviation of the number of pens Chris buy that write well?
d. what is the probability Chris buys 10 pilot pens?
e. what is the probability that the number of pen Chris buys is an even number that is at least 6?
In: Statistics and Probability
4-"What is the probability that someone you know will
die from COVID-19 this year?" and give your opinion.
Hint: You take for example the region (Tripoli,
Beyrouth...) where you live, the number of confirmed cases in this
region and the population. N represents the total number of cases
infected in the region, and p is the probability of death in
Lebanon. You calculate the P(X=1).
5- The lock down has decreased the number of infected
cases while the herd immunity has increased slightly the number of
cases again. Do you think that the herd immunity with some
restrictions can be appropriate to limit the COVID-19
infection
Please answer these two questions
completely.
In: Statistics and Probability
The expected number of births at a rural hospital is one per day. Assume that births occur independently and at a constant rate.
Use R to the draw the pmf of the number of births per day at this hospital.
Find the probability of observing at least 3 births in a day.
Find the probability of observing at most 5 births in a week.
At a larger hospital, the expected number of births per day is 17.4. Assume that births occur independently and at a constant rate. On average, how long do we have to wait until a birth at this hospital?
What is the distribution of the total number of births per day at both of these two hospitals (the sum of births at each of the hospitals)? State any assumptions that you are making.
In: Math
In: Math
Consider the missile allocation problem (MAP) with discretized time. (a) For MAP, an extreme case may be to maximize the probability of shooting down only those ASMs targeting the high value ships, ignoring the rest. How can you modify MAP model to accomplish that situation? (b) The probability of no leaker may be a very small figure, when there is a large number of attacking ASMs. For such cases, modify the objective function for maximizing the expected number of ASMs shot down.
In: Advanced Math
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)
μ = 4; σ = 2
P(3 ≤ x ≤ 7) =
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)
μ = 22; σ = 4.4
P(x ≥ 30) =
In: Statistics and Probability
. A snow tubing area has 400 snow tubes that are used each day. Each tube has as 1% chance of needing repair after each day of snow tubing.
a. Calculate the exact probability that there will not be any snow tubes needing repair after a day.
b. Calculate the mean and standard deviation of the number of snow tubes needing repair on each day.
c. Calculate the approximate probability that the number of snow tubes needing repair will be 10 or more.
In: Statistics and Probability
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)
μ = 22; σ = 3.4
P(x ≥ 30) =
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)
μ = 4; σ = 2
P(3 ≤ x ≤ 6) =
In: Statistics and Probability
Provided a standard sequence of n independent Bernoulli trials in which the probability of success is θ and the probability of failure is 1−θ.
If A represents the observed number of success and B represents the observed number of failures, (with A+B = n), then find I(θ), the Fisher information matrix. (Hint: Recall that the sum of n Bernoulli trials is a Binomial random variable. Also assume that n, A and B are fixed and so the only unknown parameter is θ, in the case I(θ) will be a scalar.)
In: Advanced Math
Assume a binomial probability distribution has
p = 0.70
and
n = 400.
(a)
What are the mean and standard deviation? (Round your answers to two decimal places.)
mean=
standard deviation =
(b)
Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
Yes, because np ≥ 5 and n(1 − p) ≥ 5.
Yes, because n ≥ 30.
Yes, because np < 5 and n(1 − p) < 5.
No, because np ≥ 5 and n(1 − p) ≥ 5.
No, because np < 5 and n(1 − p) < 5.
(c)
What is the probability of 260 to 270 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
(d)
What is the probability of 290 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
(e)
What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate.The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations. The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of calculations.The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less accurate.
In: Statistics and Probability