Statistics Math Question
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1) An insurance representative has appointments with 4 prospective clients tomorrow. From past
experience, she knows that the probability of making a sale on any appointment is .20. According
to the binomial distribution, what is the
a) probability that she will sell a policy to 2 of the 4 prospective clients?
b) probability that she will sell a policy to at least 2 of the 4 prospective clients?
c) expected number of policies she will sell and what is the standard deviation?
2) The lengths of the sardines received by a certain cannery have a mean of 4.62 inches and a
standard deviation of .23 inch. Assume the population is normally distributed. What percent of
sardines is
a) over 5 inches in length?
b) between 4.35 and 4.85 inches in length?
3) In a sample of 40 adults, the average number of seconds it took to open a temper-resistant aspirin
bottle was = 20.6 seconds and s = 5.71 seconds. Construct a 95 percent confidence interval for the
mean, number of seconds it takes to open the aspirin bottle.
4) According to the Bureau of the Census, the mean annual income of government employees is
$35,000. There is some doubt that this mean is representative of incomes of government employees
living in the San Francisco Bay area. Based on a sample of 49 government employees yielding a
mean of $35,600 and a standard deviation of $1400, at the .05 level of significance, test whether
there is sufficient evidence to conclude that the mean annual income of government employees
living in the Bay area is different than the national average.
5) It is claimed that a new treatment for prolonging the lives of cancer patients is more effective
than the standard one. Records of earlier research show the mean survival period to have been up
to 4.3 years with the standard treatment. The new treatment is administered to a sample of 20
patients, and the durations of their survival are recorded. The sample mean is 4.6 years, and the
standard deviation is 1.2 years. Can the standard treatment of up to 4.3 years be rejected, at
the 1% level of significance? Is there enough evidence to support your claim?
6) Discuss methods of probability sampling and characteristics of good surveys.
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experience, she knows that the probability of making a sale on any appointment is .20. According
to the binomial distribution, what is the
a) probability that she will sell a policy to 2 of the 4 prospective clients?
b) probability that she will sell a policy to at least 2 of the 4 prospective clients?
c) expected number of policies she will sell and what is the standard deviation?
2) The lengths of the sardines received by a certain cannery have a mean of 4.62 inches and a
standard deviation of .23 inch. Assume the population is normally distributed. What percent of
sardines is
a) over 5 inches in length?
b) between 4.35 and 4.85 inches in length?
3) In a sample of 40 adults, the average number of seconds it took to open a temper-resistant aspirin
bottle was = 20.6 seconds and s = 5.71 seconds. Construct a 95 percent confidence interval for the
mean, number of seconds it takes to open the aspirin bottle.
4) According to the Bureau of the Census, the mean annual income of government employees is
$35,000. There is some doubt that this mean is representative of incomes of government employees
living in the San Francisco Bay area. Based on a sample of 49 government employees yielding a
mean of $35,600 and a standard deviation of $1400, at the .05 level of significance, test whether
there is sufficient evidence to conclude that the mean annual income of government employees
living in the Bay area is different than the national average.
5) It is claimed that a new treatment for prolonging the lives of cancer patients is more effective
than the standard one. Records of earlier research show the mean survival period to have been up
to 4.3 years with the standard treatment. The new treatment is administered to a sample of 20
patients, and the durations of their survival are recorded. The sample mean is 4.6 years, and the
standard deviation is 1.2 years. Can the standard treatment of up to 4.3 years be rejected, at
the 1% level of significance? Is there enough evidence to support your claim?
6) Discuss methods of probability sampling and characteristics of good surveys.
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