Question

The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

Answer 1

The letter t occurs more than 26 times on approximately 420 of these pages.

Answer 2

The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

A. The letter t occurs less than 26 times on approximately 170 of these pages. 

B. The letter t occurs less than 26 times on approximately 15 of these pages. 

C. The letter t occurs more than 26 times on approximately 420 of these pages. 

D. The letter t occurs more than 26 times on approximately 80 of these pages.

.Answer: 
mean = 44 
sd = 18 
that means that "26" is 1 s.d. down, or at the 16th %ile 


so, there is a .16 chance that "t" will occur less than 26 times on any single page. 
consequently, there is a .84 chance that it will occur more than 26 times on any single page. 

Using that information, and knowing that 16% of 500 is 80, and 84% of 500 is 420, can you see where "C" is correct?