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The population of scores from a standardized test forms a normal distribution with a mean of...

The population of scores from a standardized test forms a normal distribution with a mean of μ = 450 and a standard deviation of σ = 50. The average test score is calculated for a sample of n = 26 students.

(a) What is the probability that the sample mean will be greater than M = 467? In symbols, what is p(M > 467)? (Round your answer to four decimal places.)


(b) What is the probability that the sample mean will be greater than M = 477? In symbols, what is p(M > 477)? (Round your answer to four decimal places.)


(c) What is the probability that the sample mean will be between M = 467 and M = 477? In symbols, what is p(467 < M < 477)? (Round your answer to four decimal places.)

math   Statistics-And-Probability   
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Answer #1

Given example Mean 450 Standard deviation = 50 a) P(M 467) = 0.5-P (0 < z <ー-) = 0.5-P(Oc z 467-450 0.5 p(0z<0.34) = 0.5-0.1331 P(M > 467) 0.3669 b) P(M > 477) = 0.5-P (0 < z <-) = 0.5-p。. 477-450 0.5- p(0 z<0.54) 0.5-0.2054 50 P(M > 477) = 0.2946 477-450 )-P (0 <z < 467-450 50 50 p (0 < z< 0.54)-p (0< <0.34) 0.2054- 0.1331 P(467 < M < 477) = 0.0723

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