SOLUTION: Scores for a common standardized college aptitude test are normally distributed with a mean of 518 and a standard deviation of 113. Randomly selected students are given a Test Prep

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Question 1198517: Scores for a common standardized college aptitude test are normally distributed with a mean of 518 and a standard deviation of 113. Randomly selected students are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.
If 1 student is randomly selected, find the probability that their score is at least 553.4.
P(X > 553.4) =
Enter your answer as a number accurate to 4 decimal places.
If 20 students are randomly selected, find the probability that their mean score is at least 553.4.
P(
¯¯¯
X
X
¯
> 553.4) =
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Using Handheld TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
P(X > 553.4) = normcdf(553.4, 9999, 518,113) = .3770 (accurate to 4 decimal places)
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If 20 students are randomly selected, find the probability that their mean score is at least 553.4.
z%28553.4%29+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29 , z+=blue+%2835.4%29%2Fblue%28113%2Fsqrt%2820%29%29 = 1.401
p(z > 1.401, df 19) = 0.0887 (accurate to 4 decimal places)