Question 1195179: Scores on an English test are normally distrubuted with a mean of 73 and a standard deviation of 6.8.
a.Five students are chosen random. Find the probability that:
-their mean score is less than 68
-their mean score is at least 72
b.If 30% of the test scores are above q marks, what is the value of q?Assume that all score take integer values
Answer by reviewermath(1029)   (Show Source):
You can put this solution on YOUR website! Scores on an English test are normally distrubuted (sic) with a mean of 73 and a standard deviation of 6.8.
a.Five students are chosen random. Find the probability that:
-their mean score is less than 68
Solution:
We can use Excel or R to answer Normal probability problems
In Excel, type =NORM.DIST(68,73,6.8/SQRT(5),TRUE) and the result is 0.0501 (rounded to 4 decimal places)
In R, type pnorm(68, mean = 73, sd = 6.8/sqrt(5))
and the result is 0.05007079
-their mean score is at least 72
Solution:
We modify the formulas in the previous part.
In Excel, type =1-NORM.DIST(72,73,6.8/SQRT(5),TRUE) and the result is 0.6289(rounded to 4 decimal places)
In R, type pnorm(72, mean = 73, sd = 6.8/sqrt(5), lower.tail = FALSE)
and the result is 0.6288592
b.If 30% of the test scores are above q marks, what is the value of q?Assume that all score take integer values
Solution:
In Excel, type =NORM.INV(0.7,73,6.8) and the result is 76.56592349.
The answer is 76 (32.95% got this score or higher) or 77 (27.82% got this score or higher).
In R, type qnorm(0.7, mean= 73, sd = 6.8) and the result is 76.56592
The answer is 76 (32.95% got this score or higher) or 77 (27.82% got this score or higher).
If you have clarifications, just email me (reviewermath yahoo). I can tutor you on the whiteboard.
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