Answer:
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and with the normal standard distribution table:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and with the normal standard distribution table:
Hey there! I'll try to provide you with my best answer.
Answer: x = 120 and y = 150
(x / y) = (4 / 5)
1) 5x = 4y
( (x + 20 ) / (y - 20) ) = (14 / 13)
cross multiply fractions
13(x + 20) = 14(y - 20)
13x + 260 = 14y - 280
2) 13x - 14y = -540
solve equation 1) for x
x = 4y/5
now substitute for x in equation 2)
13(4y/5) - 14y = -540
multiply both sides of = by 5
52y - 70y = -2700
-18y = -2700
y = 150
x = 4(150) / 5 = 120
x = 120 and y = 150
check answers (proof):
120 / 150 = 12 / 15 = 4 / 5
(120+20) / (150-20) = 140 / 130 = 14 / 13
Answer:
Step-by-step explanation:
X^2-22x-48=0
x^2-24x+2x-48=0
x(x-24)+2(x-24)
(x+2)(x-24)
Solve by grouping if you are able to find distinct factors that multiply to the last term and add to the middle term...this method is rather easy with easy to manage numbers. Complete the square if you cannot find distinct factors that multiply to the last term and add to the middle term. Completing the square helps when the equation is in the form of a parabola.
Answer:
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