SOLUTION: 7. The serum cholesterol levels in milligrams/deciliter (mg/dL) in a certain Mediterranean population are found to be normally distributed with a mean of 154 and a standard deviati
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-> SOLUTION: 7. The serum cholesterol levels in milligrams/deciliter (mg/dL) in a certain Mediterranean population are found to be normally distributed with a mean of 154 and a standard deviati
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Question 1027266: 7. The serum cholesterol levels in milligrams/deciliter (mg/dL) in a certain Mediterranean population are found to be normally distributed with a mean of 154 and a standard deviation of 28. Answer the following:
(a) Determine the z-score for a person from this population that has a cholesterol level of 135. Then find the z-score for someone whose cholesterol level is 217.
(b) If x represents a possible cholesterol level from this population, find P(x > 135).
(c) Find P(135 < x < 217) and give an interpretation of this value.
(d) The top 11% of all people in this group have cholesterol levels that make them "at-risk" for heart problems. Determine the raw-score cholesterol level which separates the at-risk people from the rest of the group.
8. Answer the following based upon the implications of the Central Limit Theorem.
(a) How does the mean of the sampling distribution of all possible sample means from a population compare numerically to the mean of the population?
(b) How does the standard deviation of the sampling distribution of all possible sample means (for a fixed sample size n) from a population compare numerically to the standard deviation of the population?
9. Let us assume that the prices of regular unleaded gasoline across the nation are normally distributed with a mean of $1.79 and a standard deviation of $0.25.
(a) Describe the shape and horizontal scaling on the graph of the distribution for the population of all regular unleaded gasoline prices (hereafter referred to simply as gas prices).
(b) If all possible samples of size 48 from the population of these gas prices are drawn and the mean is found for each sample, describe the shape and horizontal scaling on the graph of the sampling distribution for these sample mean values as theorized by the Central Limit Theorem.
(c) Find the probability that the price from a single randomly selected gas station will be more than $2.00. Based upon your results, would it be unusual to find an individual gas station where the price is more than $2.00? Explain.
(d) Find the probability that the mean from 15 randomly selected gas stations will be more than $2.00. Based upon your results, would it be unusual to find a sample of 15 randomly selected gas stations where the average price is more than $2.00? Explain.
10. A 90 % confidence interval for a situation is developed and is given as follows: 49 < µ < 71.
(a) Give the value of the sample mean that was used in developing this interval.
(b) Give the value of the margin of error that was used in developing this interval .
11. Calculate the appropriate critical z-value for each of the following confidence levels?
(a) 95% confidence level:
(b) 88% confidence level:
12. Does a confidence interval for µ built from some collected sample mean get wider or narrower if:
(a) the percent of desired confidence (confidence level) increases from 85% to 90%?
(b) the size of the sample used to produce the confidence interval is decreased?
(c) the standard deviation σ gets smaller?
13. A random survey of 280 registered voters revealed that 224 of them plan on voting for the incumbent. Find a 96% confidence interval for the proportion of all registered voters who plan on voting for the incumbent. Does it appear statistically valid to conclude that more than 50% of all registered voters plan on voting for the incumbent? Why or why not?
