Probability that the sample mean rent is less than $2,918.03 is 0.050154
We are given that the Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2886. Assume the standard deviation is $586.
Also, a real estate firm samples 94 apartments.
Let X = sample mean rent
The sample mean's z-score probability distribution is provided by;
Z = X-u/σ/[tex]\sqrt{n}[/tex] ~ N(0,1)
where, u= population mean monthly rent = $2,886
σ = standard deviation = $586
n = sample of apartments = 94
Now, the probability that the sample mean rent is less than $2,918.03 is given by = P( < $2,918.03)
P( < $2,918.03) = P(Z < 0.52)= 0.050154
The above probability is calculated using z table by looking at value of x = 0.52 in the z table which have an area of 0.050154
Therefore, probability that the sample mean rent is less than $2,918.03is 0.050154
Learn more about Z-score :
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