SOLUTION: A magazine article states that in a study of 64 students, average teenager reads 5.5 books a year with a standard deviation of 2 books. What is the probability that the average t

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Question 1198237: A magazine article states that in a study of 64 students, average teenager reads 5.5 books a year with a standard deviation of 2 books. What is the probability that the average teenager actually reads less than 5 books?
One of the following is the correct answer. Which one?
A) 0.0228 (2.28%)
B) 0.9772 (97%)
C) 0.5987 (59.87%)
D) 0.4013 (40.13%(
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
Normal Distribution (continuous curve) µ = 5.5 and σ = 2
probability that the average teenager actually reads less than 5 books?
Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
P(x<5) = normcdf(-9999,5,2,5.5) = .4013
0r
area to the 'left' of z = (5-5.5_/2 = -.25, P(z<.25) = .4013
Would include reading 4.5 books, for example
IF the variable x < 5 needed to be a whole number:
Then, p(x < 5 ) = p( x ≤ 4) = .2266 would work
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.


            As the problem is presented in this post,  the problem is  INCORRECT.
            The solution by  @ewatrrr is  INCORRECT,  too.
            To learn  WHY,  read my solution below to the end. 


" . . . less than 5 books "  means that the problem, ACTUALLY, asks


    +--------------------------------------------------------+
    |   What is the probability that the average teenager    |
    |          actually reads 4 or less books ?              |
    +--------------------------------------------------------+


Therefore, the correct formula expression is

    P = normalcfd(-9999, 4, 5.5, 2)


and it is equal to  0.2266.     ANSWER

                        Solved.


The correct answer in this problem is P = 0.2266 (rounded).

It is not in the list - - - therefore,  the problem is presented incorrectly in the post.

@ewatrrr calculated  P = normalcfd(-9999, 5, 5.5, 2)  instead of  P = normalcfd(-9999, 4, 5.5, 2),  giving incorrect answer.


                     In joking form, regarding this problem,
                     I would say that it is a double trap.



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