Suppose that the duration of a particular type of criminal trial is

| March 31, 2017

Question
1) Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 23 days and a standard deviation of 6 days.

· Part (a)

In words, define the random variable X.

the length, in days, of a criminal trial
the length, in hours, of a criminal trial
the mean time of all trials
the number of trials that last 23 days

· Part (b)

Give the distribution of X.
X ~
( ___ , ___)

· Part (c)

If one of the trials is randomly chosen, find the probability that it lasted more than 26 days. (Round your answer to four decimal places.)

Sketch the graph.

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Write the probability statement: P ( ___ , ___ )

· (Part (d)

76% of all of these types of trials are completed within how many days? (Round your answer to two decimal places.)

days

2) The length of time to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes.

Eighty percent of the time, it takes more than how many minutes to find a parking space? (Round your answer to two decimal places.)

min

3) The average length of a maternity stay in a U.S. hospital is said to be 2.1 days with a standard deviation of 0.8 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

In words, define the random variable X.

the number of children born in a U.S. hospital
the length of a maternity stay in a U.S. hospital, in days
the average length of a maternity stay, in days
the average number of children born in a U.S. hospital

4) The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.7 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

In words, define the random variable X.

the length of a maternity stay in a U.S. hospital, in days
the average number of children born in a U.S. hospital
the average number of women admitted to a hospital
the average length of a maternity stay in a U.S. hospital, in days

5) The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.7 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

Give the distribution of X.

(Round your standard deviation to two decimal places.)

X ~ __ ( __ , __ )

6) The average length of a maternity stay in a U.S. hospital is said to be 2.2 days with a standard deviation of 0.8 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

Is it likely that an individual stayed more than 5 days in the hospital?

Yes
No

7) The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.8 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

Is it likely that the average stay for the 80 women was more than 5 days?

Yes
No

8) The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.7 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

Which is more likely?

An individual stayed more than 5 days.
The average stay of 80 women was more than 5 days.

9) Which of the following is NOT TRUE about the distribution for averages?

The mean, median, and mode are equal.
The curve is skewed to the right.
The area under the curve is one.
The curve never touches the x-axis.

10)The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $2.19 and a standard deviation of $0.12. Twenty-five gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 25 gas stations.

What is the distribution to use for the average cost of gasoline for the 25 gas stations? (Round your standard deviation to three decimal places.)

X ~ ___ ( ___ , ___ )

11) The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $2.29 and a standard deviation of $0.08. Twenty-five gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 25 gas stations.

What is the probability that the average price for 25 gas stations is over $2.37?

The probability is almost zero.
0.0668
0.1587
0.8413
The probability is almost one.

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