Question

The answer for this problem is B (according to my practice worksheet), however, when I tried it, I got 0.6833. Help with this?

B) No 31) The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properti es. 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 investment property? A) 0.9099 31) B) 0.1335 C) 0.2236 D) 0.7764

Answer 1

Any of the answers given do not match.

Using Normal approximation to Binomial distribution, the number of homes to be used as investment property follows Normal distribution with mean = np = 800 * 0.23 = 184 and standard deviation =

Vnp(1-2) = 800 * 0.23 + (1 – 0.23)

= 11.90294

Probability that between 175 and 200 homes are going to be used as investment property

= P(175 < X < 200)

= P(X < 200) - P(X < 175)

= P[Z < (200 - 184) / 11.90294] - P[Z < (175 - 184) / 11.90294]

= P[Z < 1.34] - P[Z < -0.76]

= 0.9099 - 0.2236

= 0.6863

If the question is for Probability that between 193 and 200 homes are going to be used as investment property

Probability that between 193 and 200 homes are going to be used as investment property

= P(193 < X < 200)

= P(X < 200) - P(X < 193)

= P[Z < (200 - 184) / 11.90294] - P[Z < (193 - 184) / 11.90294]

= P[Z < 1.34] - P[Z < 0.76]

= 0.9099 - 0.7764

= 0.1335