1. A continuous random variable can take on any value within a given interval on
ID: 3255647 • Letter: 1
Question
1. A continuous random variable can take on any value within a given interval on the real line (or x-axis).
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2. A standard normal distribution is a normal distribution with any mean and a standard deviation of 1.
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3. Simple random sampling is a sampling method which ensures that every combination of n members of the population has an equal chance of being selected.
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MULTIPLE CHOICE QUESTIONS: Circle the letter which gives the best answer.
Worth 3 points each.
4. Which of the following is NOT a characteristic or a property of the normal probability distribution:
a. two parameters, the mean m and standard deviation s, determine the location and shape of the distribution
b. the highest point is at the mean, which is also the median and the mode
c. the distribution is symmetric about the mean
d. approximately 95.5% of the values will be within two standard deviations of the mean
e.none of the above; all are characteristics
5. Which of the following is a key property of the sampling distribution of the sample mean:
a. the sampling distribution is centered on the mean of the population
b. for large enough samples, the shape of the sampling distribution will be approximately normal
c. the standard deviation of the sampling distribution can be computed as the population standard deviation divided by the square root of the sample size
d. all of the above
e. none of the above
PROBLEM SETS: These problems involve calculations. Show your work and indicate your answer. Partial credit will be given. Worth 6 points each.
Use the Excel file titled “MATH 310 ADP Quiz 4 Problems Spring 2014” located in the Public (P:)/Statistics Courses/ MATH 310 ADP Quizzes folder.
6. The useful life of electrical circuits produced by your company has a uniform distribution defined by the probability density function:
1/100 for x values between 1000 and 1100 hours
f(x) =
0 everywhere else
where x = values for the random variable “useful circuit life in hours”
a. Determine the probability that useful circuit life will be between 1060 and 1085 hours.
b. Determine the probability that useful circuit life will be at least 1020 hours.
c. Determine the mean (expected value), the variance, and the standard deviation of the “useful circuit life” random variable.
7. The germination time for a newly developed seed has a normal distribution, with a mean germination time of 16.4 days and a standard deviation of 2.2 days. What percentage of the seeds have a germination period
a. between 15 and 18 days?
b. less than 12 days?
c. 99% of the seeds have a germination period of at least ________ days.
8. Brill’s Deli owns a fleet of four delivery trucks. The odometer readings for the four trucks are shown below:
Truck J K L M
Reading (000s miles) 50 50 100 100
a. Show the six equally likely samples of size 2 that could be selected from this truck population and calculate the mean odometer reading for each of the 6 samples.
b. Produce a table showing the sampling distribution of the sample mean.
c. Produce a bar chart of the sampling distribution.
Explanation / Answer
Solution:-
1. A continuous random variable can take on any value within a given interval on the real line (or x-axis).
True
2. A standard normal distribution is a normal distribution with any mean and a standard deviation of 1.
False
(It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one.)
3. Simple random sampling is a sampling method which ensures that every combination of n members of the population has an equal chance of being selected.
True
4. Which of the following is NOT a characteristic or a property of the normal probability distribution:
d. approximately 95.5% of the values will be within two standard deviations of the mean
(About 95% of the area under the curve falls within 2 standard deviations of the mean.)
5. Which of the following is a key property of the sampling distribution of the sample mean:
b. for large enough samples, the shape of the sampling distribution will be approximately normal.
6. The useful life of electrical circuits produced by your company has a uniform distribution defined by the probability density function:
1/100 for x values between 1000 and 1100 hours
f(x) =
0 everywhere else
where x = values for the random variable “useful circuit life in hours”
a. Determine the probability that useful circuit life will be between 1060 and 1085 hours.
P(1060<x<1085) = (0.01)25 < 0.000001
b. Determine the probability that useful circuit life will be at least 1020 hours.
P(x > 1020) > 0.99999
c. Determine the mean (expected value), the variance, and the standard deviation of the “useful circuit life” random variable.
Expected value = 1
Variance = 0
Standard deviation = 0
7. The germination time for a newly developed seed has a normal distribution, with a mean germination time of 16.4 days and a standard deviation of 2.2 days. What percentage of the seeds have a germination period
a. between 15 and 18 days? 0.5042
b. less than 12 days? 0.0228
c. 99% of the seeds have a germination period of at least 22 days.
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