Find the probability that a randomly selected individual earned less than $24,000.
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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%
what about randomly selected sample of 10 individuals, the mean salary was less than $24,000.
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