Solve the following:
Q1. Consider a population with a mean =73.6 and a standard deviation=5.38
A. Calculate the z-score for sample mean=72.7 from a sample size of 45.
Q2. Given a level of confidence of 99% and a population standard deviation of 7, answer the following:
A. What other information is necessary to find the sample size(n)?
B. Find the Maximum error of estimate (E) if n = 74.
Q3. A sample of 75 golfers showed that their average score on a particular golf course was 91.32 with a standard deviation of 6.85. Answer each of the following and state the final answer to at least two decimal places.
A. Find the 95% confidence interval of the mean score for all 75 golfers.
B. FInd the 95% confidence interval of the mean score for all golfers if this is a sample of 120 golfers instead of a sample of 75.
C. Which confidence interval is larger and why?
Q4. Assume that the population of heights of female college students is approximately normally distributed with mean of 67.26 inches and standard deviation of 5.96 inches. A random sample of 78 heights is obtained.
A. Find the mean and standard error of the x distribution.
B. Find P (x > 67.50)
Q5. The diameters of peaches in a certain orchard are normally distributed with a mean of 4.01 inches and a standard deviation of 0.44 inches. Show all work.
A. What percentage of the peaches in this orchard is larger than 3.94 inches?
B. A random sample of 100 peaches is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 3.94 inches?
Q6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 5.31, how large a sample is needed to get the desired information to be accurate with 0.63 decibels?