Question

The national association of realtors estimates that 23% of all homes purchased in 2004 were considered investments properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that between 175 and 200 homes are going to be used as a investment property?

Answer 1

Solution:

Given:

p = probability of all homes purchased in 2004 were considered investments properties = 0.23

n = sample size = 800

We have to find the probability that between 175 and 200 homes are going to be used as a investment property

That is:

Here X = Number of homes are going to be used as a investment property follows a Binomial distribution.
Since sample size is large , we can use Normal approximation to Binomial.

Find Mean and Standard deviation.

Mean:

Standard Deviation:

We need to use continuity correction to use Normal approximation to Binomial.

That is we add or subtract 0.5 from x values.

Here we subtract 0.5 from lower limit and add 0.5 in upper limit, so that both limit values would fall in range of x values.

Now find z scores:

Thus we get:

Look in z table for z = 1.3 and 0.09 as well as for z = -0.8 and 0.00 and find area.

P( Z< -0.80) = 0.2119

P( Z < 1.39) =0.9177

thus

the probability that between 175 and 200 homes are going to be used as a investment property is 0.7058