(10 points) The scores of students on the ACT college entrance examinations in a
ID: 3310514 • Letter: #
Question
(10 points) The scores of students on the ACT college entrance examinations in a recent year had a normal distribution with mean -18.4 and standard deviation = 5.6. (a) What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher? ANSWER: For parts (b) through (d), consider a simple random sample (SRS) of 45 students who took the test. (b) What are the mean and standard deviation of the sample mean score , of these 45 students? The mean of the sampling distribution for is: The standard deviation of the sampling distribution for is: of 23? (c) What z-score corresponds to the mean score ANSWER (d) What is the probability that the mean score ANSWER: of these students is 23 or higher?Explanation / Answer
Mean is 18.4 and s is 5.6
a) z is given as (x-mean)/s
thus P(x>23)=P(z>(23-18.4)/5.6)=P(z>0.82) or 1-P(z<0.82)
from normal ditstribution table we get 1-0.7939=0.2061
b) N=45 , mean is 18.4
standard error is s/sqrt(N)=5.6/sqrt(45)=0.834799
c) z for 23 is (23-18.49)/0.834799=5.4025
d) P(xbar>23)=P(z>(23-18.49)/0.834799)=P(z>5.4) =1-P(z<5.4) =0
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