th mean 5 point) The scores o students on the S T college entrance examinations
ID: 3318288 • Letter: T
Question
th mean 5 point) The scores o students on the S T college entrance examinations a a certain h n schoo had a norma dist but on (a) What is the probability that a single student randomly chosen from all those taking the test scores 547 or higher? ANSWER and Standard de lation For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score E, of 30 students? The mean of the sampling distribution for is: The standard deviation of the sampling distribution for is: (c) What z-score corresponds to the mean score ANSWER: of 547? (d) What is the probability that the mean score ANSWER: of these students is 547 or higher?Explanation / Answer
Mean is 542.9 and s is 26.9
a) z is given as (x-mean)/s thus P(x>547)=P(z>(547-542.9)/26.9)=P(z>0.15) or 1-P(z<0.15)
from normal distribution table we get 1-0.5596=0.4404
b) for a sample size of 30, mean is same as 542.9
the standard error SE=s/sqrt(N)=26.9/sqrt(30)=4.91
c) z=(547-542.9)/4.91=0.835
d) P(z>0.835)=P(z>0.84) or 1-P(z<0.84)
from normal distribution table we get 1-0.7995=0.2005
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