Scores on a chemistry final exam are normally distributed with a mean of 280 and a...
Scores on a chemistry final exam are normally distributed with a mean of 280 and a standard deviation of 20. Determine the percentage of samples of size 4 that will have mean scores within 14 points of the population mean score of 280. Round to two decimal places.
A.
99.48 %
B.
83.84 %
C.
91.92 %
D.
51.60 %
Homework Answers
Solution :
Given that,
mean = 
= 280
standard deviation = 
= 20
=
/ 
n = 20/
4 = 10
= P[(-14) /10 < (
-
)
/
< (14) / 10)]
= P(-1.4 < Z < 1.4)
= P(Z < 1.4) - P(Z < -1.4)
= 0.9192 - 0.0808
= 0.8384 = 83.84%
percentage = 83.84%
option B. is correct
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