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Chapter 5: Q.5.30 (page 348)
Use the following information to answer the next eight exercises. A distribution is given as .
What is the theoretical standard deviation?
The theoretical standard deviation is.
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Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years.
a. Find the probability that a light bulb lasts less than one year.
b. Find the probability that a light bulb lasts between six and ten years.
c. Seventy percent of all light bulbs last at least how long?
d. A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest two percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place?
e. If a light bulb has lasted seven years, what is the probability that it falls within the year.
Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery.
a. Define the random variable. X = _________________________________.
b. Is X continuous or discrete?
c. X ~ ________
d. On average, how long would you expect one car battery to last?
e. On average, how long would you expect nine car batteries to last, if they are used one after another?
f. Find the probability that a car battery lasts more than 36 months.
g. Seventy percent of the batteries last at least how long?
Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.
What is being measured here?
According to a study by Dr. John McDougall of his live-in weight loss program, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let鈥檚 suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. a. Define the random variable. X = _________ b. X ~ _________ c. Graph the probability distribution. d. f(x) = _________ e. 渭 = _________ f. 蟽 = _________ g. Find the probability that the individual lost more than ten pounds in a month. h. Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month. i. P(7 < x < 13|x > 9) = __________. State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.
What is the area under f(x) if the function is a continuous probability density function?
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