In the given normal distribution with a mean of 100 and standard distribution of 15, 95% of values will fall between 70 and 130 using the Empirical rule of 95%.
Step-by-step explanation:
A normal distribution with a mean of 100 and a standard distribution of 15 is given.
We will find where 95% of data fall in the given normal distribution.
It states that in a normal distribution approximately 95% of observations fall within two standard deviations from the mean on both sides of the normal curve.
The mean in a normal distribution is the center of the normal curve.
The standard deviation in a normal distribution is the distance from the mean to the required point on either side.
We have,
Mean = 100
Standard deviation = 15
Applying the 95% rule we get,
On the right side of the normal curve
Mean + 2 x standard deviation = 100 + 2x 15 = 100 + 30 = 130.
On the left side of the normal curve,
Mean - 2 x standard deviation = 100 - 2x15 = 100 - 30 = 70.
Thus, we see that by using the Empirical rule of 95%, 95% values will fall between 70 and 130.
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