A professor believes that individual scores on a certain test will have mean 75
ID: 3332110 • Letter: A
Question
A professor believes that individual scores on a certain test will have mean 75 and standard deviation 15.  If they teach a class of 50 students (presumably sampled at random from this student population), what is the probability that...
...the class mean will be less than 70. ?
...the class mean will be 90 or more. You can round your answer to three decimal places (or ten for that matter!) here. ?
On the other hand, suppose the professor is teaching a large lecture section of this class with 400 students. What is the probability the class mean will be 76 or more?
Same question for a super-large-lecture class with 1500 students.
?
Explanation / Answer
Mean = 75
Stdev = 15
n = 50, initially
a. P(X<70)
= P(Z< (70-75) / (15qrt(50))
= P(Z<-2.36)
= 0.0091
b.
P(X>=90)
= P(Z>= (90-75)/(15/sqrt(50))
= P(Z>=7.07)
= .00769E-10
c.
P(X>=76) = ? SInce student sample size is quiet high i.e. 400 , we don't need to use Standard error. P(X>=76) = P(Z>= (90-76)/15)
= 1-.8247
= 0.1753
If the class is 1500 students big, then the answer is gonna be same. We use the Z distribution like in part c. to solve the problem. The more is the sameple size the normal-like distribution is it.
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