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%.
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 normal curve's centre corresponds to the mean in a normal distribution.
The distance between the mean and the necessary point on either side in a normal distribution is known as the standard deviation.
Given: Mean = 100
Standard deviation = 15
Apply the 95% rule we get,
The normal curve's right side
Mean + 2 x standard deviation
= 100 + 2x 15
= 100 + 30
= 130.
The normal curve's left side,
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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