5. A real estate agent is looking at the selling prices of homes in Stockton, CA

Question

5. A real estate agent is looking at the selling prices of homes in Stockton, CA. He believes the data to be normally distributed, and has found that the data has q=$123500 and o=$63200. Use this information to answer his questions.

A) What is the probability that a randomly selected house sells for less than $144000?

B) What is the probability that a randomly selected house sells for between $60000 and $150000?

C) What is the probability that a randomly selected house sells for over $250000?

D) What is the probability that a randomly selected house sells for exactly $123500?

E) What is the probability that a randomly selected house sells for between $100000 and $275000?

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 123500
standard Deviation ( sd )= 63200
a.
P(X < 144000) = (144000-123500)/63200
= 20500/63200= 0.3244
= P ( Z <0.3244) From Standard Normal Table
= 0.6272
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 60000) = (60000-123500)/63200
= -63500/63200 = -1.0047
= P ( Z <-1.0047) From Standard Normal Table
= 0.1575
P(X < 150000) = (150000-123500)/63200
= 26500/63200 = 0.4193
= P ( Z <0.4193) From Standard Normal Table
= 0.6625
P(60000 < X < 150000) = 0.6625-0.1575 = 0.505
c.
P(X > 250000) = (250000-123500)/63200
= 126500/63200 = 2.0016
= P ( Z >2.0016) From Standard Normal Table
= 0.0227

d. since normal is continuous for particular point it is zero

e.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 100000) = (100000-123500)/63200
= -23500/63200 = -0.3718
= P ( Z <-0.3718) From Standard Normal Table
= 0.355
P(X < 275000) = (275000-123500)/63200
= 151500/63200 = 2.3972
= P ( Z <2.3972) From Standard Normal Table
= 0.9917
P(100000 < X < 275000) = 0.9917-0.355 = 0.6367

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.