Basic Statistics

78

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

6.10

6.11

THE NORMAL DISTRIBUTION

Does the stem and leaf display of the hemoglobin data given in Table 4.1 appear

to be approximately normally distributed? Plot a histogram, box plot, and a

normal probability or a normal q-q plot and compare the results.

Problems 6.3-6.8 refer to the following situation: A population of women’s

weights is approximately normally distributed with a mean of 140 lb and a

standard deviation of 20 lb.

What percentage of women weigh between 120 and 160 lb?

If samples of size 16 are drawn from the population of women’s weights, what

percentage of the sample means lie between 120 and 160 lb?

What is the probability that a sample mean from a sample size 16 lies above

145 lb?

Find P95, the 95th percentile for the population of women’s weights.

Find P95, the 95th percentile for the population of means for samples of size

16.

In Problems 6.4 and 6.6, what justification is there for using the tables of the

normal distribution?

A quality control inspector examines some bottles of a herbal medication to

determine if the tablets are all within stated limits of potency. The results were

that 13 bottles had 0 tablets out of limits, 26 bottles had 1 tablet, 28 bottles

had 2 tablets, 18 bottles had 3 tablets, 9 bottles had 4 tablets, 4 bottles had 5

tablets, and 2 bottles had 6 tablets out of limits. In all, n = 100 bottles were

tested. Give two transformations that are suitable transformations to try that

might achieve a distribution somewhat closer to a normal distribution for the

number of tablets per bottle that are outside the stated limit.

From Table A.2, read what z is for an area up to SO, .95. .975, and .995.

What two values of z should be used to obtain a .025 in each of the two tails in

Table A.2?

REFERENCES

Afifi, A. A., Clark, V. and May, S. [2004]. Computer-Aided Multivariate Analysis, 4th ed.,

Cleveland, W. S. [1993]. Visualizing Data, Summit, NJ: Hobart Press, 56.

Fox, I. and Long, J. S. [1990]. Modern Methods ofData Analysis, Thousand Oaks, CA: Sage,

Tukey, J. W. [ 19771. Exploratory Data Analysis, Reading, MA: Addison-Wesley, 57-93.

Boca Raton, FL: Chapman & Hall/CRC, 57-63.

80-87.