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luda_lava [24]
3 years ago
8

4.) The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform dis

tribution with A = 20 and B = 50. What is the probability that preparation is within 2 minutes of the mean time?
Mathematics
1 answer:
Jet001 [13]3 years ago
8 0

Answer:

P(35-2 < X 35+2) = P(33< X< 37)= P(X

And using the cumulative distribution function we got:

P(35-2 < X 35+2) = P(33< X< 37)= P(X

The probability that preparation is within 2 minutes of the mean time is 0.134

Step-by-step explanation:

For this case we define the following random variable X= (minutes) for a lab assistant to prepare the equipment for a certain experiment , and the distribution for X is given by:

X \sim Unif (a= 20, b =50)

The cumulative distribution function is given by:

F(x) = \frac{x-a}{b-a} , a \leq X \leq b

The expected value is given by:

E(X) = \frac{a+b}{2} = \frac{20+50}{2}=35

And we want to find the following probability:

P(35-2 < X 35+2) = P(33< X< 37)

And we can find this probability on this way:

P(35-2 < X 35+2) = P(33< X< 37)= P(X

And using the cumulative distribution function we got:

P(35-2 < X 35+2) = P(33< X< 37)= P(X

The probability that preparation is within 2 minutes of the mean time is 0.134

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