Answer:
The Normal distribution is a continuous probability distribution with possible values all the reals. Some properties of this distribution are:
Is symmetrical and bell shaped no matter the parameters used. Usually if X is a random variable normally distributed we write this like that:
The two parameters are:
who represent the mean and is on the center of the distribution
who represent the standard deviation
One particular case is the normal standard distribution denoted by:
Example: Usually this distribution is used to model almost all the practical things in the life one of the examples is when we can model the scores of a test. Usually the distribution for this variable is normally distributed and we can find quantiles and probabilities associated
Step-by-step explanation:
The Normal distribution is a continuous probability distribution with possible values all the reals. Some properties of this distribution are:
Is symmetrical and bell shaped no matter the parameters used. Usually if X is a random variable normally distributed we write this like that:
The two parameters are:
who represent the mean and is on the center of the distribution
who represent the standard deviation
One particular case is the normal standard distribution denoted by:
Example: Usually this distribution is used to model almost all the practical things in the life one of the examples is when we can model the scores of a test. Usually the distribution for this variable is normally distributed and we can find quantiles and probabilities associated
Answer:
<em>99.93%</em>
Step-by-step explanation:
<u>Probability of Independent Events</u>
Given the probability of success of each detector is 0.84 independently of the others, their combined success/failure probability can be computed with the product rule.
We can calculate the required probability by using the binomial distribution, but it's easier to calculate the probability of the negated event an subtract from 1.
We want to know the probability that a least one of the 4 systems detects the occurrence of theft. That probability is the sum of the probabilities that one of them, two of them, three of them or all of them succeed. The negated event is that NONE of them actually detects the theft. Being p the individual probability of success, p=0.84. Being q the probability of failure, q=0.16.
The probability that none of the systems detect the theft is
Thus, the probability that at least one of the systems detect the theft is
That means a 99.93%
Answer:
Step-by-step explanation:
Total pencils = 48
Total erasers = 72
If we put 1 pencil and 1.5 eraser in each pouch then total pouches = 48 pouches
Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))
The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))
The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))
x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))
Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))
x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))
Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))
((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))
Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:
Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
Answer:
X Y
8 4
14 7
6 3
Step-by-step explanation:
y = x/2
x = 2y
