A town has 500 real estate agents. The mean value of the properties sold in a ye

Question

A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000, and the standard deviation is $400,000 . A random sample of 100 agents is selected, and the value of the properties they sold in a year is recorded.

a. What is the standard error of the sample mean?

b. What is the probability that the sample mean exceeds $840,000?

c. What is the probability that the sample mean exceeds $767,000?

d. What is the probability that the sample mean is between $788,000 and $807,000 ?

Explanation / Answer

a)

standard error = 400000/sqrt(100) = 40000

b)

P(X>840000) = P(Z > 840000 - 800000/40000) = P(Z > 1) = 0.1587

c)

P(X > 767000) = P(Z > 767000-800000/40000) = P(Z > -0.825) =0.7953

d)

P( 807000 > X > 788000) = P(Z < 807000-800000/40000) - P(788000-800000/40000)

= P(Z < 0.175 ) - P(Z < -0.3)

= 0.5695 - 0.3821

= 0.1874

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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