Statistics for decision making
Please use 200 words to answer the following 6 questions:
1. What is the difference between the probability distribution of a discrete random variable and that of a continuous random variable? Let xx be a continuous random variable. What is the probability that xx assumes a single value such as a? For a continuous probability distribution explain why the following holds true: P(a

1)A random sample is
to be selected from a population with mu = 100 and standard deviation = 10.
Determine the standard deviation of the x-bar sampling distirbution for a
sample size of n = 9. (three decimal places)
2)A random sample is to be selected from a
population with mu = 100 and standard deviation = 10. Determine the standard
deviation of the x-bar sampling distirbution for a sample size of n = 400.
(three decimal places)
3)Suppose that a random samle of size 64 is to
be selected from a population with mean 40 and standard deviation 5.
What is the mean of the sampling distribution?
4) Suppose that a random samle of size 64 is to
be selected from a population with mean 40 and standard deviation 5.
What is the standard deviation of the sampling
distribution?
5)Suppose that a random sample of size 64 is to
be selected froma population with mean 40 and standard deviation fo 5.
What is the approximate probability that xbar
will be within .5 of the population mean mu? (round to 4 decimal places)
6)Suppose that a random sample of size 64 is to
be selected froma population with mean 40 and standard deviation fo 5.
What is the approximate probability that xbar
will differ from mu by more than .7? (4 decimal places please)
7)In the library on a university campus, there
is a sign in the elevator that indicates a limit of 16 persons. Further more,
there is a weight limit of 2500 pounds. Assume the average weight of students,
faculty and staff on campus is 150 pounds, the standard devaiton is 27 pounds
and that the distribution is approximately normal, If a random sample of 16
persons from the campus is taken
What is the expected value of the smaple man of
their weights
8)In the library on a university campus, there
is a sign in the elevator that indicates a limit of 16 persons. Further more,
there is a weight limit of 2500 pounds. Assume the average weight of students,
faculty and staff on campus is 150 pounds, the standard devaiton is 27 pounds
and that the distribution is approximately normal, If a random sample of 16
persons from the campus is taken.
What is the standard deviation of the sampling
distribution
9)In the library on a university campus, there
is a sign in the elevator that indicates a limit of 16 persons. Further more,
there is a weight limit of 2500 pounds. Assume the average weight of students,
faculty and staff on campus is 150 pounds, the standard devaiton is 27 pounds
and that the distribution is approximately normal, If a random sample of 16
persons from the campus is taken.
What average weight for tehse 16 people will
result in the total weight exceeding the weight limit of 2500 pounds. (two
decimal places)
In other words if the average persons weight is
greater than or equal to _____
10)In the library on a university campus, there
is a sign in the elevator that indicates a limit of 16 persons. Further more,
there is a weight limit of 2500 pounds. Assume the average weight of students,
faculty and staff on campus is 150 pounds, the standard devaiton is 27 pounds
and that the distribution is approximately normal, If a random sample of 16
persons from the campus is taken
What is the chance that a random sample of 16
persons on the elevator will exceed teh weight limit? (four decimal places)
11) Use the pull out table(Z-TABle)
in your book and list the critical value (z*) for a 95% confidence Interval
(two decimal places).

12)Using your z table and a graph of a normal
curve, calculate the z* value for an 88% confidence interval

13)Using the student’s t table, find the
critical value (t*) for a sample of 21 students with a confidence interval of
98%

14) . A medical researcher from the National
Institute of Health has collected samples on the life expectancies of people
who are long-time smokers and those who are nonsmokers. The sample data is
summarized in the table below.

Group sample size sample mean standard deviation

smokers 50 67.6 5
nonsmokers 60 74.6 3.5

Do I need a z interval or a t interval (just
enter z or t in lower case letters)

15)A medical researcher from the National
Institute of Health has collected samples on the life expectancies of people
who are long-time smokers and those who are nonsmokers. The sample data is
summarized in the prev table. Compute a 95% confidence interval for the mean life
expectancy of a smoker.

16)Compute a 95% confidence interval for the
mean life expectancy of a nonsmoker using prev table

17) A study of the price of a gallon of heating
oil reported the following statistics from random samples of prices on the east
coast and the west coast#

Coast sample size sample mean sample standard
deviation

east 90 1.096 .035
west 160 1.123 .036

Do I use a z or a t critical value here? type in
z or t

18)Compute a 95% confidence interval for the
mean price of a gallon of heating oil on the east coast from prev table

19)Compute a 95% confidence interval for the
mean price of a gallon of heating oil on the west coast.