order? c. Find the waiting time at which only 10% of the customers will continue to...

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order? c. Find the waiting time at which only 10% of the customers will continue to...

At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.

Required

a. What is the probability density function for this uniform distribution?

b. What is the probability of waiting no more than 3 minutes?

c. What is the probability that the subway arrives in the first minute and a half?

d. What is the median waiting time for this subway?

math Statistics-And-Probability

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Answer 1

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Answer #1

Solution: We are given that waiting time for a subway is uniformly distributed between 1 and 5 minutes.

a. What is the probability density function for this uniform distribution?

Answer:

Let x be the waiting time for a subway, then the probability density function for this uniform distribution is given below:

b. What is the probability of waiting no more than 3 minutes?

Answer: The probability of waiting no more than 3 minutes is:

$small P(xleq 3)=int_{1}^{3}xrac{1}{4}dx$

small =rac{3-1}{4}

-= 0.5

c. What is the probability that the subway arrives in the first minute and a half?

Answer: The probability that the subway arrives in the first minute and a half is:

1.5 1 P(1 < x < 1.5) = x-d2

1.5 -1

0.5 -= 0.125

d. What is the median waiting time for this subway?

Answer: The median waiting time for this subway is:

Median 5 + 1

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Answer 2

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