(1 point) The scores of students on the SAT college entrance examinations at a c

Question

(1 point) The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean = 551 and standard deviation = 27. (a) What is the probability that a single student randomly chosen from all those taking the test scores 556 or higher? ANSWER: e men andsampe meen n ,130 students? The mean of the sampling distribution for is: (c) What z-score corresponds to the mean score x of 556? ANSWER: (d) What is the probability that the mean score X of these students is 556 or higher? ANSWER:

Explanation / Answer

Mean is 551 and s is 27. z is calculated as (x-mean)/s

a) P(x>556)=P(z>(556-551)/27)=P(z>0.19) or 1-P(z<0.19). from normal distribution table we get 1-0.5753=0.4247

b) Mean is 551 for sample. and standard deviation for sample is 27/sqrt(30)=4.9295

c) z score for 556 =(556-551)/4.9295=5/4.9295=0.1014

d) P(x>556)=P(z>0.1014) or 1-P(z<1.0)=1-0.8413=0.1587

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