Question

In a normal distribution of measurements having a mean of 500 feet and a standard deviation of 50 feet, what percent of the distribution falls between 490 and 520 feet?

Answer 1

This is a normal distribution question with
$\\Mean (\mu)= 500 \\Standard\;Deviation (\sigma)= 50$
Since we know that
$z_{ score } = \frac{x-\mu}{\sigma}$
x1 = 490
x2 = 520
P(490.0 < x < 520.0)=?
$\\ z_1 = \frac {490.0-500.0}{50.0} \\ z_1 = -0.2 \\ z_2 = \frac {520.0-500.0}{50.0} \\ z_2 = 0.4$
This implies that
P(490.0 < x < 520.0) = P(-0.2 < z < 0.4) = 0.2347
PS: you have to refer z score table to find the final probabilities.
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