Based on the last question, respond the following:What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000?

0.9886

Step-by-step explanation:

The mean of the distribution of sample means is given as μₓ

μₓ = μ = $117000

Standard deviation of the distribution of sample means = σₓ

σₓ = (σ/√n)

where n = sample size = 40

σₓ = (25000/√40) = $3952.85

The probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000

P(|x - 117000| < 10000) = P(107000 < x < 127000)

This is a normal distribution problem

We convert the $107000 and $127000 into standardized scores

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For $107000

z = (x - μ)/σ = (107000 - 117000)/3952.85 = -2.53

For $127000

z = 2.53

To determine the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000

P(107000 < x < 127000) = P(-2.53 < z < 2.53)

We'll use data from the normal probability table for these probabilities

P(107000 < x < 127000) = P(-2.53 < z < 2.53) = P(z < 2.53) - P(z < -2.53) = 0.99430 - 0.00570 = 0.9886

Hope this Helps!!!

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step-by-step explanation: