Question

The mean cost of renting an apartment in a city is $2000 per month with a standard deviation of $300. Let ?̅ denote the mean cost of rent for a random sample of 60 apartments in this city.

(a) 0.0985 (b) 0.1783 (c) 0.4013 (d) 0.05987 (e) 0.9015

Step 1

Denote *X* as the mean cost of renting an apartment in a city. It is given that *X* is distributed, with mean *μ* = $2000 and standard deviation *σ* = $300.

A random sample of 60 apartments are taken.

As the sample size is large (>30), it can be assumed that the mean cost of renting an apartment in a city follows normal distribution with mean *μ* = $2000 and standard deviation *σ* = $300.

Let X bar be the mean cost rent for the sample. It is known that,

Step 2

Therefore, in this situation,

Step 3

The probability that the sample mea...

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