MA 132 Nova Academy of Cosmetology Chapter 9 Standard Deviation Handout Questions I have handout and I will attach all the slides and definitions will need

MA 132 Nova Academy of Cosmetology Chapter 9 Standard Deviation Handout Questions I have handout and I will attach all the slides and definitions will need to answer I need the answers for the questions under each question and I need it in word file please Section 8.1 Questions
1. Suppose you have a population with mean µ = 100 and standard deviation σ = 10 and you take
every sample of size n from this population.
(a) Suppose the population was normally distributed and n = 16.
i. What is the mean and standard deviation of the sampling distribution of the mean?
µx̄ =
σx̄ =
ii. Will the sampling distribution of the mean be normally distributed?
(b) Suppose the population was not normally distributed and n = 64.
i. What is the mean and standard deviation of the sampling distribution of the mean?
µx̄ =
σx̄ =
ii. Will the sampling distribution of the mean be normally distributed?
(c) Suppose the population was not normally distributed and n = 16.
i. What is the mean and standard deviation of the sampling distribution of the mean?
µx̄ =
σx̄ =
ii. Will the sampling distribution of the mean be normally distributed?
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2. The average life span for a person in a particular country is 78.2 years with a standard deviation
of 16 years.
(a) Do you think the population distribution will be normal, skewed left, or skewed right?
(b) Suppose we take a sample of size n = 45.
i. Will the distribution of the sample means be normal? Why or why not?
ii. What is the probability of getting a sample mean of 83 years or more?
iii. What is the probability of getting a sample mean of 75 years or less?
iv. In what interval is the middle 80% of sample average life spans?
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Section 9.2 Questions
3. Determine the point estimate of the population mean and the margin of error of the confidence
interval, when the lower bound is 22 and the upper bound is 28.
4. A simple random sample of size n is drawn from a population that is normally distributed. The
sample mean is found to be x̄ = 50 and the sample standard deviation is found to be s = 8.
(a) Construct a 98% confidence interval for µ if the sample size is n = 20. What is the margin
of error?
(b) Construct a 98% confidence interval for µ if the sample size is n = 15. What is the margin
of error?
(c) How does decreasing the sample size affect the margin of error?
(d) Construct a 95% confidence interval for µ if the sample size is n = 20. What is the margin
of error?
(e) How does decreasing the level of confidence affect the margin of error?
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5. Suppose the scores of a new standardized math test are Normally distributed with an unknown
mean and an unknown standard deviation. A simple random sample of n = 25 students yields
an average score of x̄ = 525 and a standard deviation of s = 60.
(a) Construct and interpret a 90% confidence interval for the population mean.
(b) Construct and interpret a 95% confidence interval for the population mean.
(c) What sample size would be needed to make the margin of error for the 90% confidence no
more than 7.
(d) What sample size would be needed to make the margin of error for the 95% confidence no
more than 7.
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