Answer:
0.9886
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!!!