A random number generator picks a number from 1 to 9 in a uniform manner.
Graph the probability distribution.
Find the 90th percentile.
The time (in minutes) until the next bus departs a major bus depot follows a distribution with
where
goes from 25 to 45 minutes.
Define the random variable.
Graph the probability distribution.
The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
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.
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.
_________. State this in a probability statement (similar to
g and
h ), draw the picture, and find the probability.
Find the 90th percentile. This means that 90% of the time, the time is less than _____ minutes.
Find the 75th percentile. In a complete sentence, state what this means. (See
j .)
Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
uniform; continuous
35 minutes
5.8 minutes
0.25
0.5
1
43 minutes
40 minutes
0.3333
According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let’s 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. (Source:
The McDougall Program for Maximum Weight Loss by John A. McDougall, M.D.)
Define the random variable.
Graph the probability distribution.
Find the probability that the individual lost more than 10 pounds in a month.
Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 12 pounds in the month.
__________. State this in a probability question (similar to g and h), draw the picture, and find the probability.
A subway train on the Red Line arrives every 8 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.
Define the random variable.
Graph the probability distribution.
Find the probability that the commuter waits less than one minute.
Find the probability that the commuter waits between three and four minutes.
60% of commuters wait more than how long for the train? State this in a probability question (similar to
g and
h ), draw the picture, and find the probability.
where
4
2.31
3.2
The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. We randomly select one first grader from the class.
Define the random variable.
Graph the probability distribution.
Find the probability that she is over 6.5 years.
Find the probability that she is between 4 and 6 years.
Find the 70th percentile for the age of first graders on September 1 at Garden Elementary School.
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Source:
OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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