Question

weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of 50. find the probability that a worker selected at random makes between $300 and $400​

Answer 1

Answer:

47.5%

Step-by-step explanation:

Find the z-scores:

z = (x − μ) / σ

z₁ = (300 − 400) / 50 = -2

z₂ = (400 − 400) / 50 = 0

300 is 2 standard deviations below the mean, and 400 is 0 standard deviations from the mean.

From the empirical rule, 95% of a normal distribution is between -2 and +2 standard deviations.  Since normal distributions are symmetrical, that means half of that is between -2 and 0 standard deviations.

95% / 2 = 47.5%