Answer:
![P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D%201-%20P%28X%3E8%29%20%3D%201-P%28X%5Cgeq%209%29%3D%201-%5BP%28X%3D9%29%2BP%28X%3D10%29%5D)
And we can find the individual probabilities like this:
And replacing we got:
![P(X\leq 8)=1-[10(0.8)^1 (1-0.8)^{1} + (0.8)^{10}]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D1-%5B10%280.8%29%5E1%20%281-0.8%29%5E%7B1%7D%20%2B%20%280.8%29%5E%7B10%7D%5D)
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by:
Solution to the problem
For this case we want this probability:

And for this case we can use the comlement rule and we got:
![P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D%201-%20P%28X%3E8%29%20%3D%201-P%28X%5Cgeq%209%29%3D%201-%5BP%28X%3D9%29%2BP%28X%3D10%29%5D)
And we can find the individual probabilities like this:
And replacing we got:
![P(X\leq 8)=1-[10(0.8)^9 (1-0.8)^{1} + (0.8)^{10}]](https://tex.z-dn.net/?f=P%28X%5Cleq%208%29%3D1-%5B10%280.8%29%5E9%20%281-0.8%29%5E%7B1%7D%20%2B%20%280.8%29%5E%7B10%7D%5D)
Answer:
Q1: I forgot measure of center but I think mean Q2: D
Step-by-step explanation:
Answer:
the smallest part is 2
Step-by-step explanation:
lets take x as the smallest part
then the largest part=3x
the middle sized part=2x
x+2x+3x=12
6x=12
x=12/6
x=2
therefore the smallest part is equal to 2
I think is
9 + x = 16 + 27
9 + x = 43
x = 52
Answer:
An airline estimates that 94% of people booked on their flights actually show up. If the airline books 77 people on the flight for which the maximum number is 75, what is the probability that the number of people who show up will exceed the capacity of the plane?
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Binomial Problem with n = 77 and p = 0.94
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P(76 <= x <= 77) = 1-P(0 <=x <= 75) = 1 - binomcdf(77,0.94,75) = 0.0504
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Cheers,
Stan H.