Respuesta :
Answer:
0.15866.
Step-by-step explanation:
We have been given that on average, electricians earn approximately μ= $54,000 per year in the united states. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ= $12,000. We are asked to find the probability that the sample mean is greater than $66,000.
First of all, we will find the z-score corresponding to 66,000 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{66000-54000}{12000}[/tex]
[tex]z=\frac{12000}{12000}[/tex]
[tex]z=1[/tex]
Now, we need to find the probability that z-score is greater than 1 that is [tex]P(z>1)[/tex].
Upon using formula [tex]P(z>A)=1-P(z<A)[/tex], we will get:
[tex]P(z>1)=1-P(z<1)[/tex]
Upon using normal distribution table, we will get:
[tex]P(z>1)=1-0.84134[/tex]
[tex]P(z>1)=0.15866[/tex]
Therefore, the probability that the sample mean is greater than $66,000 would be 0.15866 or approximately [tex]15.87\%[/tex].
