##### Statistics: Find the probability that a randomly selected individual earned less than \$24,000.

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The average annual salary in Pennsylvania was \$25,000 in 1992. Assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was \$3,000.

Find the probability that a randomly selected individual earned less than \$24,000.

Nov 6th, 2015

We know  the mean  u = 25,000  s = 3000.  Where  X is a random variable representing annual salary and is normally distributed.

We want to find  Pr( X < 24000).

To do this, we Standardize this normal distribution:

Pr( X < 24000) = Pr( (X- u)/s < (24000 - u)/s ) =  Pr( Z <  (24000 - 25000)/3000) = Pr(Z < -1/3) = 0.3707 (approximately)

According to the Standard Normal graph  The probability that corresponds to  Z < -0.33  is 0.3707

Therefore the probability that a random person earns less than \$24,000 is 37%

If we want more accuracy, the probability is 37.1%

Nov 6th, 2015

what about randomly selected sample of 10 individuals, the mean salary was less than \$24,000.

Nov 6th, 2015

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Nov 6th, 2015
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Nov 6th, 2015
May 24th, 2017
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