# statistics assignment 64

*Medical: Blood Protoplasm*Porphyrin is a pigment in the blood protoplasm and other body fluids that is significant in body energy and storage. Let*x*be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults,*x*is approximately normally distributed with mean and standard deviation . What is the probability that 20 healthy adults will have an average porphyrin level

- less than34?

- greater than 42?

- between34 and 42?

2.) *Totals instead of Averages: Airplane Takeoff Time* The taxi and takeoff time for commercial jets is a random variable*x *with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after another, and that they take off one at a time on a given runway. What is the probability that for 10 jets on a given runway, total taxi and take off time will be

a.)less than 70 minutes? *Hint: Either multiply and by the sample size *n*or divideby *n*.

b.) more than 2 hours?

*Confidence Intervals*

3.)*Profits: Retail* Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of one thousand dollars per employee) for companies in retail sales. Assume thousand dollars.

4.4 6.5 4.2 8.9 8.7 8.1 6.1 6.0 2.6 2.9 8.1 -1.9

11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 -6.0 1.5 2.9 4.8

-1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2

- Calculate the mean.

- Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for, the average annual profit per employee for retail sales.

*Interpretation:*Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits per employee are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part b.

*Hypothesis Testing*

4.) ** Matches: Number per Box** A match company sells matchboxes that are supposed to have an average of 40 matches per box, with a standard deviation of 9. A random sample of 94 of the companyâ€™s matchboxes gives an average of 43.1 matches per box. Using a 1% level of significance, can you say that the average number of matches in the box is more than 40?

5.) The National Center for Health Statistics reports that the systolic blood pressure for males 35 to 44 years of age has a mean 128 and a standard deviation 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure in this sample is Is this evidence that the companyâ€™s executives have a different mean blood pressure from the general population? Suppose that we know that blood pressures follow a Normal distribution with standard deviation . Use a significance level of .

6.) *Medical : Red Blood Cell Volume* Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell mean is about ml/kg. Red Blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the results were

32 25 41 35 30 37 29

The sample mean is ml/kg. Let *x* be a random variable that represents Rogerâ€™s red blood cell volume. Assume that *x* has a normal distribution and . Do the data indicate that Rogerâ€™s red blood cell volume is different (either way) from ml/kg? Use a 0.01 level of significance.