Suppose that, on average, electricians earn approximately μ= $54,000 per year in the united states. Assume that the distribution for electri

Question

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?

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Amara 3 weeks 2021-09-26T19:01:04+00:00 1 Answer 0

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    2021-09-26T19:02:22+00:00

    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<A), we will get:

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

    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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