The scores of students on the SAT college entrance examinations at a certain hig
ID: 3389406 • Letter: T
Question
The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean mu = 544.7 and standard deviation sigma = 27.9.
(a) What is the probability that a single student randomly chosen from all those taking the test scores 551 or higher? ANSWER:
For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.
(b) What are the mean and standard deviation of the sample mean score ar x, of 35 students? The mean of the sampling distribution for ar x is: The standard deviation of the sampling distribution for ar x is:
(c) What z-score corresponds to the mean score ar x of 551? ANSWER:
(d) What is the probability that the mean score ar x of these students is 551 or higher? ANSWER:
Explanation / Answer
Mean ( u ) =544.7
Standard Deviation ( sd )=27.9
Normal Distribution = Z= X- u / sd ~ N(0,1)
a)
P(X < 551) = (551-544.7)/27.9
= 6.3/27.9= 0.2258
= P ( Z <0.2258) From Standard Normal Table
= 0.5893
P(X > = 551) = (1 - P(X < 551)
= 1 - 0.5893 = 0.4107
b)
Number ( n ) = 35
Standard Deviation ( sd )=27.9/ Sqrt ( 35 ) = 4.716
c)
P(X = 551) = (551-544.7)/27.9/ Sqrt ( 35 )
Z = 6.3/4.716= 1.3359
d)
P(X < 551) = (551-544.7)/27.9/ Sqrt ( 35 )
= 6.3/4.716= 1.3359
= P ( Z <1.3359) From Standard NOrmal Table
= 0.9092
P(X > = 551) = 1 - P(X < 551)
= 1 - 0.9092 = 0.0908