Suppose you're given a data set that classifies each sample unit into one of four categories: A, B, C, or D. You plan to crea
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Answer:
A) probability of failure in next 100 hours given that it has been tested for 500 hours without failure is 0.181
B) probability that exactly two have the metabolic defect is 0.03
Step-by-step explanation:
Part A)
Let X be a exponentially random variable with mean = μ = 500 hrs
For exponential distribution:
λ = 1/μ
λ = 0.002
We have to find the probability of failure in the next 100 hours given that assembly has been tested for 500 hours without a failure.
Using memory less property of exponential distribution:
using
Chances of occurrence of metabolic defect = 5%
P(C) = .05
No. of randomly selected infants = n =6
We have to find the probability that exactly two have the metabolic defect
⇒x = 2
Using binomial probability density function:
P =
probability that exactly two have the metabolic defect is 0.03
9514 1404 393
Answer:
(a) 4/3
(b) y -3 = 4/3(x -1)
(c) y -3 = -3/4(x -1)
(d) r = 5
Step-by-step explanation:
a) The slope is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -3)/(4 -1) = 4/3
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b) The radius is normal to the circle. The point-slope form of the equation for a line can be useful here:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
For slope 4/3, the line through point (1, 3) will have the equation ...
y -3 = 4/3(x -1) . . . . point-slope equation of the normal
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c) The tangent is perpendicular to the radius. It will have a slope that is the opposite reciprocal of the slope of the radius: -1/(4/3) = -3/4.
y -3 = -3/4(x -1) . . . . point-slope equation of the tangent
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d) The radius can be found from the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -1)² +(7 -3)²) = √(3² +4²) = √25 = 5
The radius of the circle is 5.
