a) A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each with probability 0.8, what is the probability that a 4-out-of-6 system functions?
b) Obtain ?(?(?−2)) where ? ~???????(?)
c) Service calls arrive at a maintenance center according to a Poisson process, with average 3.1 calls per minute.
(i) Obtain the probability that no more than 4 calls arrive in a minute.
(ii) Obtain the probability that more than 7 calls arrive in a three-minute interval
In: Statistics and Probability
Please post the work so I can understand the process :) Thanks!
a. What is the probability of receiving exactly one call during a one-minute interval?
b. What is the probability of receiving at most 2 calls during a one-minute interval?
c. What is the probability of receiving at least two calls during a one-minute interval?
d. What is the probability of receiving exactly 4 calls during a five-minute interval?
In: Statistics and Probability
Hank would like to know how many customers are entering his propane store within a given timeframe. Prior data indicate that on average 8 customers arrive in a given hour.
a. Create the appropriate probability distribution below for 0-12 arrivals.
b. What is the probability that 8 or fewer customers will arrive in the next hour?
c. What is the probability that exactly 10 customers arrive in the next hour?
d. What is the probability that more than 12 customers will arrive in the next hour?
e. How likely is it that Hank has a "large crowd" entering his store in the next hour?
In: Statistics and Probability
The probabilities of an individual having a particular blood type are listed below.
Type A .4
Type B .3
Type AB .25
Type O .05
9. Find the probability that a randomly selected individual will have type A or type b blood.
10. Find the probability that a randomly selected individual will have a blood type other than type AB.
11. Find the probability that a randomly selected individual will have type AB or type O.
12. Find the probability that a randomly selected individual has a blood type other than type A or type B.
In: Statistics and Probability
5. A driver encounters two traffic lights on the way to work
each morning. Each light is either red, yellow, or green. The
probabilities of the various combinations of colors is given in the
following table:
|
Second Light |
|||
|
First Light |
R |
Y |
G |
|
R |
0.31 |
0.02 |
0.18 |
|
Y |
0.02 |
0.03 |
0.03 |
|
G |
0.14 |
0.04 |
0.23 |
a) What is the probability that the first light is red?
b) What is the probability that the second light is green?
c) Find the probability that both lights are of the same color.
d) Given that the first light is red, find the probability that the second light is green.
In: Statistics and Probability
|
Johnson Company is preparing a bid on a new construction project. Two other contractors will be submitting bids for the same project. |
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Based on past bidding practices, bids from other contractors can be described by the following probability distributions: |
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Contractor A: Uniform probability distribution between $500,000 and $1,000,000. |
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Contractor B: Normal probability distribution with a mean bid of $700,000 and a standard deviation of $100,000. |
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a. If Johnson Company submits a bid of $750,000, what is the probability Butler will obtain the bid. Simulate 1000 trials of the contract bidding process. Note: Johnson's bid must be less than BOTH A and B. |
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In: Statistics and Probability
According to the Bureau of Transportation Statistics, 81.9% of American Airlines flights were on time in 2017. Assume this percentage still holds true for American Airlines. For the next
44 flights from American Airlines, use the normal approximation to the binomial distribution to complete parts a through d.
a.) Determine the probability that fewer than 34 flights will arrive on time.
b.) Determine the probability that exactly 32 flights will arrive on time.
c.) Determine the probability that 25, 26, 27, or 28 flights will arrive on time.
d.) Determine the probability that 28, 29, 30, 31, or 32 flights will arrive on time.
In: Math
|
Female |
Male |
||
|
Accounting |
68 |
56 |
124 |
|
Administration |
91 |
40 |
131 |
|
Economics |
5 |
6 |
11 |
|
Finance |
61 |
59 |
120 |
|
225 |
161 |
386 |
b. Find the probability that the selected student is an administration major or a finance major.
c. Find the probability that the selected student is an administration major or a female.
d. Find the probability that the selected student is finance major, given he is a male.
In: Statistics and Probability
Alice and Bob are supposed to meet in the cafeteria. Alice
arrives at a random time between
noon and 1pm, and wait for 15 minutes upon her arrival and then
leaves. Bob also also arrives
at a random time between noon and 1 pm, but waits up to 20 minutes
and then leaves.
(a) What is the probability that Bob arrives before 12:20?
(b) What is the probability that Alice and Bob meet?
(c) If Bob arrives later than Alice, what is the probability that
they meet?
(d) Suppose that Alice and Bob have managed to meet. What is the
probability that Bob
has arrived before 12:20?
In: Math
An email system sends incoming mail to either the In-Folder (I) or the Trash Folder (T). You classify incoming mail as Useful (U), in which case you want it sent to I, or as a Nuisance (N) in which case you would like it sent to T. If incoming mail is U, the system sends it to T with probability 0.1. If the incoming mail is N, the system sends it to I with probability 0.05. Suppose a proportion 0.35 of your incoming mail is N.
What is the probability that an incoming mail is sent to T?
What is the probability that an incoming mail is U given that it is sent to T?
In: Math