Question

Cheap-As-Dirt Rental Company advertises that the average cost of a rental they find for undergraduate students at the University of Oregon is $580 with a standard deviation of $75 (Let us assume the rents are approximately Normally distributed.) The Department of Consumer Protection will investigate the company if, when they choose a sample of students, they find that the average rental cost for those students is $610 or more. Assuming that the company is advertising truthfully, what is the probability that the company will be investigated if the Department of Consumer Protection samples 8 clients? (Round your answer to 4 decimal places, to the ten thousandths place.)vg

Answer 1

Solution :

Let X be a random variable which represents the rental cost of undergraduate students at the University of Oregon, that is advertised by a rental company.

Given that, X is normally distributed.

X ~ N(580, 75²)

Mean(μ) = $580

SD(σ) = $75

Sample size (n) = 8

Now the rental company will be investigated if sample mean of the rental cost of 8 students is greater than or equal to $610.

Hence, we have to find P(x̅ ≥ $610).

(Where, x̅ is sample mean rental cost of 8 students.)

We know that if, X ~ N(μ, σ²) then, x̅ ~ N(μ, σ²/n).

And if x̅ ~ N(μ, σ²/n) then,

Using "pnorm" function of R we get, P(Z ≥ 1.1314) = 0.1289

Hence, the company will be investigated if the Department of Consumer Protection samples 8 clients is 0.1289.

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