Questions from Calculus


Q: Which route should the student in Exercise 29 take if she leaves

Which route should the student in Exercise 29 take if she leaves home at 7:26 a.m.? Exercise 29: A student with an eight o’clock class at the University of Maryland commutes to school by car. She has...

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Q: A certain type of bolt must fit through a 20-millimeter

A certain type of bolt must fit through a 20-millimeter test hole or else it is discarded. If the diameters of the bolts are normally distributed, with µ = 18.2 millimeters and σ = .8 millimeters, wha...

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Q: The Math SAT scores of a recent freshman class at a university

The Math SAT scores of a recent freshman class at a university were normally distributed, with µ = 535 and σ = 100. (a) What percentage of the scores were between 500 and 600? (b) Find the minimum sco...

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Q: Let X be the time to failure (in years) of

Let X be the time to failure (in years) of a computer chip, and suppose that the chip has been operating properly for a years. Then, it can be shown that the probability that the chip will fail within...

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Q: Recall that the median of an exponential density function is that number

Recall that the median of an exponential density function is that number M such that Pr (X ≤ M) = ½. Show that M = (ln 2)/k. (We see that the median is less than the mean.)

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Q: If the lifetime (in weeks) of a certain brand of

If the lifetime (in weeks) of a certain brand of lightbulb has an exponential density function and 80% of all lightbulbs fail within the first 100 weeks, find the average lifetime of a lightbulb.

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Q: An exponential random variable X has been used to model the relief

An exponential random variable X has been used to model the relief times (in minutes) of arthritic patients who have taken an analgesic for their pain. Suppose that the density function for X is f (x)...

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Q: The computations of the expected value and variance of an exponential random

The computations of the expected value and variance of an exponential random variable relied on the fact that, for any positive number k, be-kb and b2 e-kb approach 0 as b gets large. That is, lim x&a...

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Q: Use the integral routine to convince yourself that ∫-∞∞ x2 f (

Use the integral routine to convince yourself that ∫-∞∞ x2 f (x) dx = 1, where f (x) is the standard normal density function. [Note: Since f (x) approaches zero so rapidly as x gets large in magnitude...

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Q: Find (by inspection) the expected values and variances of the

Find (by inspection) the expected values and variances of the exponential random variables with the density function given. 3e-3x

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