The time that it takes for a calculus student to answer

For a restaurant, the time it takes to deliver pizza (in minutes) is uniform over the interval (25, 37). Determine the proportion of deliveries that are made in less than half an hour.

It is known that the weight of a random woman from a community is normal with mean 130 pounds and standard deviation 20. Of the women in that community who weigh above 140 pounds, what percent weigh over 170 pounds?

One thousand random digits are generated. What is the probability that digit 5 is generated at most 93 times?

Let X, the lifetime of a light bulb, be an exponential random variable with parameter . Is it possible that X satisfies the following relation? P (X 2) = 2P (2 < X 3). If so, for what value of ?

The time that it takes for a computer system to fail is exponential with mean 1700 hours. If a lab has 20 such computer systems, what is the probability that at least two fail before 1700 hours of use?

Let X be a uniform random variable over the interval (0, 1). Calculate E( ln X).

Suppose that the diameter of a randomly selected disk produced by a certain manufacturer is normal with mean 4 inches and standard deviation 1 inch. Find the distribution function of the diameter of a randomly chosen disk, in centimeters.

Let X be an exponential random variable with parameter . Prove that P ( X + ) P (0 X ).

The time that it takes for a calculus student to answer all the questions on a certain exam is an exponential random variable with mean 1 hour and 15 minutes. If all 10 students of a calculus class are taking that exam, what is the probability that at least one of them completes it in less than one hour?

Determine the value(s) of k for which the following is a density function. f (x) = kex2+3x+2 , < x < .

The grades of students in a calculus-based probability course are normal with mean 72 and standard deviation 7. If 90, 80, 70, and 60 are the respective lowest, A, B, C, and D, what percent of students in this course get As, Bs, Cs, Ds, and Fs?

The number of minutes that a train from Milan to Rome is late is an exponential random variable X with parameter . Find P ! X > E(X)" .

In a measurement, a number is rounded off to the nearest k decimal places. Let X be the rounding error. Determine the probability distribution function of X and its parameters.

Suppose that the weights of passengers taking an elevator in a certain building are normal with mean 175 pounds and standard deviation 22. What is the minimum weight for a passenger who outweighs at least 90% of the other passengers?

The breaking strength of a certain type of yarn produced by a certain vendor is normal with mean 95 and standard deviation 11. What is the probability that, in a random sample of size 10 from the stock of this vendor, the breaking strengths of at least two are over 100?

The number of phone calls to a specific exchange is a Poisson process with rate 23 per hour. Calculate the probability that the time until the 91st call is at least 4 hours.

Let X be a uniform random variable over the interval (1 , 1 + ), where 0 < < 1 is a given parameter. Find a function ofX, say g(X), so that E 4 g(X)5 = 2.

A beam of length $ is rigidly supported at both ends. Experience shows that whenever the beam is hit at a random point, it breaks at a position X units from the right end, where X/$ is a beta random variable. If E(X) = 3$/7 and Var(X) = 3$2/98, find P ($/7 < X < $/3).