Three men are trying to hold a ferocious lion still for the veterinarian. The lion, in the center,is wearing a collar with three
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Complete question :
A company is manufacturing highway emergency ares. Such ares are sup- posed to burn for an average of 20 minutes. Every hour a sample of ares is collected, and their average burn time is determined. If the manufacturing process is working cor- rectly, there is a 68% chance that the average burn time of the sample will be between 14 minutes and 26 minutes. The quality engineer in charge of the process believes that if 4 of 5 samples fall outside these bounds then this is a signal that the process might not be performing as expected. Each morning the sampling begins anew. Let X denote the number of samples drawn in order to obtain the fourth sample whose average value is outside of the above bounds. Find the probability that for a given morning X = 5, hence there seems to be a problem right away.
Answer:
0.0285
Step-by-step explanation:
We are to find the probability for a given morning that X = 5
From the question, we could see that there is a 68% chance that the average burn time of the sample will be between 14 minutes and 26 minutes and the success of the process is obtained after the fourth or fifth sample.
Thus, r = 4; q = 0.68
The probability average burn time falls outside p will be:
p = 1 - 0.68 = 0.32
The random variable X follows negative binomial distribution.
Therefore,
Where, x = 5
r = 4
p = 0.32
Substituting figures in the equation, we have:
= 0.0285
The probability that for a given morning X = 5 is 0.0285
The exact distance between two points L=(1,-3) and P=(8,-7)is 8.062 units, is obtained by formula and graphical method.
Step-by-step explanation:
The given is,
Two points are L=(1,-3) and P=(8,-7)
Step:1
By graphical method,
First point L (1,-3)
The values of x=1 and y=-3 noted in the graph
Second point P(8, -7)
The values of x=8 and y=-7 noted in the graph
Now join the points L and P, in the graph,
Distance between two points are 8.1 units
( OR )
Step:2
By formula method,
Distance =
Where,
L (1,-3) are ()
P (8,-7) are ()
Substitute the values,
=
=
=
=
Distance = 8.06225 units
Result:
The exact distance between two points L=(1,-3) and P=(8,-7)is 8.062 units, is obtained by formula and graphical method.
