Help with an Sampling Distribution of Mean problem

[From: ] [author: ] [Date: 11-05-09] [Hit: ]

) 12 randomly selected men were given a review course before taking the SAT test. If their mean score is 576.5, is there a strong evidence to support the claim that the course is actually effective?z-score = (576.5-509)/112 = 0.......

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112.

(a) If 1 man is randomly selected, find the probability that his score is at least 576.5

(b) If 12 men are randomly selected, find the probability that their mean score is at least 576.5

c.) 12 randomly selected men were given a review course before taking the SAT test. If their mean score is 576.5, is there a strong evidence to support the claim that the course is actually effective? (Yes or No)

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qa
z-score = (576.5-509)/112 = 0.6
P(z>0.6) = 0.2743 <--------

qb
standard error = 112/sqrt(12)
z-score = 0.6*sqrt 12 = 2.08
P[z>2.08] = 0.0188 <--------

qc
yes

1

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