Determine the mean, the standard deviation, the variance, and the five-number summary. Using the fence rule, determine if data set has any outliers. Draw a histogram. Properly name the graph and the axes.

ASSIGNMENT D

The center thickness (in mils) of a sample of twenty-five contact lenses are given below

0.3978                   0.4019                   0.4031                   0.4044                   0.3984                   0.3972                   0.3981

0.3947                   0.4012                   0.4043                   0.4051                   0.4016                   0.3994                   0.3999

0.4062                   0.4048                   0.4071                   0.4015                   0.3991                   0.4021                   0.4009

0.3988                   0.3994                   0.4016                   0.4010

Using this data set and RStudio answer the five following questions

1. Determine the mean, the standard deviation, the variance, and the five-number summary.
2. Using the fence rule, determine if data set has any outliers.
3. Draw a histogram. Properly name the graph and the axes.
4. Draw a boxplot (horizontal).
5. Construct a qqplot and a qqline and determine if this data set is approximately normal.
6. To experimentally verify the central limit theorem, take 1000 random samples of size from a population that is distributed  exponentially with .  To this end, you must show

 

• The histogram of the distribution is approximately normal.

HINT: Use the following session commands:

> xbar <- rep(0,1000)

> for(i in 1:1000){xbar[i]=mean(rexp(33, 3))}

> hist(xbar, prob = TRUE)

• Its expected value is .

HINT: Use

        > mean(xbar)

What is the expected value of an exponential distribution?

• Its variance is .

HINT: Use

        > sd(xbar)

What is the standard deviation of an exponential distribution?