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svet-max [94.6K]
2 years ago
7

Suppose 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. What is the probability that the sample mean is greater than $66,000?
Mathematics
1 answer:
11111nata11111 [884]2 years ago
4 0

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.

z=\frac{x-\mu}{\sigma}

z=\frac{66000-54000}{12000}

z=\frac{12000}{12000}

z=1

Now, we need to find the probability that z-score is greater than 1 that is P(z>1).

Upon using formula P(z>A)=1-P(z, we will get:

P(z>1)=1-P(z

Upon using normal distribution table, we will get:

P(z>1)=1-0.84134

P(z>1)=0.15866

Therefore, the probability that the sample mean is greater than $66,000 would be 0.15866 or approximately 15.87\%.

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