Question

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most 175 homes are going to be used as investment property? Round to four decimal places, if necessary.

Answer 1

Solution:

Given that,

P = 23% =0.23

1 - P =1-0.23= 0.77

n = 800

Here, BIN ( n , P ) that is , BIN (800 , 0.23)

then,

n*p = 800*0.23= 184 > 5

n(1- P) = 800*0.77 = 616 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P =184

Standard deviation = =n*p*(1-p) = 800*0.23*0.77 = 141.68

We using countinuity correction factor

P( X a ) = P(X < a + 0.5)

P(x < 175.5) = P((x - ) / < (175.5-184) /141.68 )

= P(z < -0.714)

= 0.2376

Probability = 0.2376