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Answer:
<em>84%</em><em> of the wage earners earn less than $14,000 each. </em>
Step-by-step explanation:
The Empirical Rule (68-95-99.7%)-
According to this around 95% of the data will fall within two standard deviations of the mean.
As the bell curve is symmetrical, so the remaining 5% will be divided into 2 equal parts. So 2.5% will be above 2 standard deviation and 2.5% will be below 2 standard deviation.
As it is given that, the top 2.5% of the wage earners earn $18,000 or more, so 18,000 is 2 standard deviation away from the mean 10,000.
i.e
We know that,
where,
X = raw score = 14,000
μ = 10,000
σ = 4,000
Putting the values,
Now, calculating the value from the z score table,
As the probability at is the area below that, so 84% of the wage earners earn less than $14,000 each.
Probably you are supposed to compute
Factorize the numerator and denominator, then simplify:
Factorize the numerator and denominator, then simplify: