A librarian estimates that the average number of books checked out by a library patron is 4, with a standard deviation of 2 books. If the number of books checked out each day approximates a normal distribution, what percent of the library patrons checked out fewer than 7 books yesterday.

Can you guys please explain to me how I'd solve this? And like show steps? I'd really appreciate it.. thanks :)

Question

A librarian estimates that the average number of books checked out by a library patron is 4, with a standard deviation of 2 books. If the number of books checked out each day approximates a normal distribution, what percent of the library patrons checked out fewer than 7 books yesterday.

Can you guys please explain to me how I'd solve this? And like show steps? I'd really appreciate it.. thanks :)

unklerhaukus · Answer

the number of results within 1 standard deviation for any normal distribution is 68.2%
then number of results within 2 standard deviations is 98.4%
results more than 2 standard deviation from the norm are 1.6%

well fewer than 7 means either 0,1,2,3,4,5,6
6 is 1 standard deviation from the average
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