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

Question

Jairo Mcdonald

Mathematics

31 May, 06:22

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

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Sanai Forbes · Answer 1

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%