Question

Suppose the length of textbooks in a library follows a bimodal distribution with a little right skewness (very mild). The mean of this distribution is 512 pages with a standard deviation of 390 pages.

For each of the following i) draw a picture. ii) label the picture with 2 axes (underneath). iii) label the shorthand for the new distribution. iv) Find the z-score. v) Find the answer.  

a1) What is the probability that a random sample of 36 textbooks has an average of 445.2 pages or less?

a2) What is the probability that a random sample of 49 textbooks has an average higher than 613.3 pages?

a3) What is the probability that a random sample of 30 textbooks has an average number of pages between 400 and 500?

a4) Do you think you could answer a1 - a4 with a sample of just 2 textbooks? Why or why not?

a5) Do you think you could answer a1-a4 with a sample of 25 textbooks? Why or why not?

a6) Describe the central limit theorem in a paragraph.  

a7) What is the formula for standard error? And what is it in relation to the central limit theorem.  

Answer 1

a4: We could not answer a1-a3 since we use central limit theorem and central limit theorem holds when sample size is large.

a5. Since sample size=25 is large so we can answer a1-a3.