The percentage of values is within the interval 111 to 139 will be "68%".
According to the question,
Mean = 125
Standard deviation = 14
Let,
The random variable be "X".
Now, the probability:
→ P(111 < X < 139) = P (111 - 125 < X - 125 < 139 - 125)
= P(-14 < X - 125 < 14)
= P(-[tex]\frac{14}{14}[/tex] < [tex]\frac{(X-125)}{14}[/tex] < [tex]\frac{14}{14}[/tex])
= P(-1 < Z < 1)
When, Distribution function "[tex]\phi[/tex]" now,
= [tex]\phi[/tex](1) - [tex]\phi[/tex](-1)
= [tex]\phi[/tex](1) - 1 + [tex]\phi[/tex](1)
= 2 × [tex]\phi[/tex](1) - 1
= 2 × 0.8413 -1
= 1.6826 - 1
= 0.6826 or,
= 68%
Thus the above answer i.e., "option C" is correct.
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https://brainly.com/question/24756209
