On your shelf, you have four books that you are planning to read in the near future. Two are fictional works, containing 212 and 379 pages, respectively, and the other two are non-fiction, with 350 and 575 pages respectively.

(a) Compute the population mean and standard deviation of the (parent) population of number of pages of the four books.

(b). Suppose that you select a simple random sample of two books from the four to take on a one-week ski trip (in case you injure yourself). Let X denote the sample mean number of pages for the two books selected. Obtain the sampling distribution of X for this sampling method, and determine its mean and standard deviation.

(c) Suppose that you randomly select one of the two fiction books and independently randomly select one of the two non-fiction books. Obtain the sampling distribution of X for this sampling method, and determine its mean and standard deviation.

(d) Which of these two sampling methods would you prefer for making an educated guess about ? Why?

Solution Preview

Hi there,

Here are my answers:

a. mean=(212+379+350+575)/4=379.
standard deviation=sqrt(((379-212)^2+(379-379)^2+(350-379)^2+(575-379)^2)/(4-1))=149.6061.

b. The distribution of ...

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