SOLUTION: The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean = 548.4 and standard deviation = 28.1 . (a) What is th

Question 1192872: The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean = 548.4 and standard deviation = 28.1 .
(a) What is the probability that a single student randomly chosen from all those taking the test scores 553 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 x
, of 35 students?
The mean of the sampling distribution for x
is:
The standard deviation of the sampling distribution for
is:
(c) What z-score corresponds to the mean score x
of 553?
ANSWER:
(d) What is the probability that the mean score x
of these students is 553 or higher?
ANSWER:

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
z>(553-548.4)/28.1=0.1637
probability z > 0.1637 is 0.4350
-
for 35 students, the mean of the sampling distribution is 548.4, no change.
the sd is original sd/sqrt(n)=4.75
-
z now is 4.6/4.75=0.97
the probability now is 0.1664
RELATED QUESTIONS
If you solve the question below, I'll be appreciated. The scores of students on the... (answered by Theo)

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are... (answered by Theo)

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are... (answered by Boreal)

Suppose the mathematics section of SAT scores for high school seniors for a specific year (answered by ewatrrr)

There are two major tests of readiness for college, the ACT and the SAT. ACT scores... (answered by Boreal)

Scores on the SAT form a normal distribution with a mean score of 500 and a standard... (answered by Theo)

Based on data from the College board SAT scores are normally distributed with a mean of... (answered by Boreal)

Amanda took the SAT and scored 680 on the mathematics part. The distribution of SAT math... (answered by jim_thompson5910)

Scores on the SAT form a normal distribution with an average of 500 and a standard... (answered by ewatrrr)