Answer:
84% of the wage earners earn less than $14,000 each.
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 [tex]2\sigma=18000-10000=8000[/tex]
[tex]\Rightarrow \sigma = 4000[/tex]
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
where,
X = raw score = 14,000
μ = 10,000
σ = 4,000
Putting the values,
[tex]Z=\dfrac{14000-10000}{4000}=\dfrac{4000}{4000}=1[/tex]
Now, calculating the value from the z score table,
[tex]P(1)=0.8413=84.13\%[/tex]
As the probability at [tex]z=1[/tex] is the area below that, so 84% of the wage earners earn less than $14,000 each.
