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1.    The following observations are DDT concentrations in the blood of 20 people:

24       26       30       35       35       38       39       40       40       41                   42       52       56       58       61       75       79            88       102     42

a. Construct the normal probability plot and comment on the                                          appropriateness of a normal probability model. Any outliers?

b. Assuming that the sample is representative for the population at large, what is the probability that a person selected at random has the DDT concentration in blood greater than 50?

2.    Determine the values z that separates the largest 3% of all the z values from the others and the smallest 3% of all the z values from the others. What can you say about these z values?

3.    In many cases the data does not follow a normal distribution closely enough to be able to make reasonably correct references using the relationship of the data with the standard normal distribution. Among the many proposed courses of action, transforming the data to get it closer to a normal distribution is quite often the method of choice. One such transformation requires to replace the each data point by its square root and perform the analysis on the transformed data.

In the following example, determine the normality of the original data, then convert the data points to their square roots and determine the normality of the transformed data. (plot Normal Probability Plots). Did the transformation have any effect on the normality of the data.

Data:

32       47       52       59       77       81       81       90       96       118     120     120     131 135         143     151     62       174     187     189     195            205     210     220     248   281 300           309     337     475