SOLUTION: A set of data is normally distributed with a mean of 44 and a standard deviation of 3.2. Which of the following statements are not true? I. 68% of the values are between 37.6 a

Question 1087372: A set of data is normally distributed with a mean of 44 and a standard deviation of 3.2. Which of the following statements are not true?
I. 68% of the values are between 37.6 and 50.4.
II. 13.5% is between 37.6 and 40.8.
III. 5% of the values are lower than 37.6 or higher than 50.4.
a. I
b. II
c. III
d. I and II
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
use the normal distribution 68-95-99.7 rule
:
68% of the values are 1 standard deviation around the mean (44-3.2, 44+3.2) = (40.8, 47.2) so I is false
:
95% of the values are within 2 standard deviations around the mean (44-6.4, 44+6.4) = (37.6, 50.4), 95 - 68 = 27, 27/2 = 13.5, so II is true
:
2.5% greater than 50.4 and 2.5% less than 37.6 = 5%, so III is true
:
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I. is the correct answer
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