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Chapter 5: Q.5.31 (page 348)
Use the following information to answer the next eight exercises. A distribution is given as .
Draw the graph of the distribution for .
the graph for required probability that isis,
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The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as .
What is ?
The time (in minutes) until the next bus departs a major bus depot follows a distribution with where goes from 25 to 45 minutes.
a. Define the random variable.
b.
c. Graph the probability distribution.
d. The distribution is (name of distribution). It is (discrete or continuous).
e.
f.
g. Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
h. Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
i. . State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.
j. Find the percentile. This means that of the time, the time is less than
k. Find the percentile. In a complete sentence, state what this means. (See part j.)
1. Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.
a. Find the probability that the time between two successive visits to the urgent care facility is less than \(2\) minutes.
b. Find the probability that the time between two successive visits to the urgent care facility is more than \(15\) minutes.
c. If \(10\) minutes have passed since the last arrival, what is the probability that the next person will arrive within the
next five minutes?
According to the American Red Cross, about one out of nine people in the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution.
a. If people arrive, how many on average would be expected to have Type B blood?
b. What is the probability that over people out of these 100 have type B blood?
c. What is the probability that more than people arrive before a person with type B blood is found?
A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. 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 commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probabilit
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