The mean selling price of senior condominiums in Green Valley over a year was $2

Question

The mean selling price of senior condominiums in Green Valley over a year was $215,000. The population standard deviation was $ 25,000. A random sample of 100 new unit sales was obtained. What is the probability that the sample mean selling price was more than $210,000? What is the probability that the sample mean selling price was between $ 213,000 and $ 217,000? Suppose that, after you had done these calculations, a friend asserted that the population distribution of selling prices of senior condominiums in Green Valley was almost certainly not normal. How would you respond?

Explanation / Answer

8a).

Standard error = sd/sqrt(n) =25000/sqrt(100) =2500

Z value for 210000, z=(210000-215000)/2500 = -2

P( mean x > 210000) = P( z >-2) =0.9772

b).

Z value for 213000, z=(213000-215000)/2500 = -0.8

Z value for 217000, z=(217000-215000)/2500 = 0.8

P( 213000<mean x< 217000) = p( -0.8<z<0.8)

=P( z<0.8) –P( z < -0.8)

= 0.7881 -0.2119

=0.5762

c).

Since sample size 100 is larger ( > 30), by central limit theorem, sample mean follows approximately normal distribution, even the distribution of the population is not normal.

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