Question

What is the probability that a random sample of 100 houses in Minneapolis will provide a sample mean within $10,000 of the population mean, $325,000

Answer 1

0.01

Explanation:

We are given;

Population mean; μ = $325,000

Sample size; n = 100

We are told that the sample mean is within $10,000 of the population mean.

Thus; if sample mean is x¯, then;

x¯ - μ = 10000

x¯ - 325000 = 10000

x¯ = 335000

Now population standard deviation is gotten from;

σ = √((x¯ - μ)²/n)

σ = √(10000²/100)

σ = 1000

In expected value probability problems, standard deviation is expressed as;

σ = √((x¯ - μ)²P(x))

Where P(x) is the probability.

Thus;

1000² = 10000² × P(x)

P(x) = 1000²/10000²

P(x) = 0.01