Question

# Assume that the selling prices of various homes in a city are normally distributed, such that...

Assume that the selling prices of various homes in a city are normally distributed, such that the m = \$676,000, and the d is \$32,000, then

a.To find the probability that the next house sold in this city would sell more than \$590,000, what is x? (x greater or less than some number)

b.To find the probability that the next house sold in this city would sell more than \$590,000, what is z? (2 decimal places)

c.What is the probability that the next house sold in this city would sell more than \$590,000? (4 decimal places)

d.To find the probability that the next house would sell between \$630,000 and \$720,000, what is x between? (lower number separated by comma and space with upper number)

e. To find the probability that the next house would sell less than \$630,000 , what is z ? (2 decimal places)

f.What is the probability that the next house would sell less than \$630,000 ? (4 decimal places)

g.To find the probability that the next house would sell less than \$720,000 , what is z ? (2 decimal places)

h.What is the probability that the next house would sell less than \$720,000? (4 decimal places

i.What is the probability that the next house would sell between \$630,000 and \$720,000? (4 decimal places)

j.In the last 35 houses sold in this city, how many were sold between \$630,000 and \$720,000? (round to next higher integer)

a)

Here we need to find

P (X >590000)

b)

The z-score for X = 590000 is

z = {590000-676000} / {32000} = -2.6875 ≈ -2.69

c)

The probability that the next house sold in this city would sell more than \$590,000 is

P(X>590000) = P(z>-2.69) = 0.9964

d)

P(630000<X<720000)

e)

The z-score for X = 630000 is

z= {630000-676000} / {32000} = -1.25

f)

The probability that the next house sold in this city would sell less than \$630,000 is

P(X<630000) = P(z<-1.25) = 0.1056

g)

The z-score for X = 720000 is

z= {720000-676000} / {32000} = 1.375

h)

The probability that the next house sold in this city would sell less than \$720,000 is

P(X<720000) = P(z<1.38) = 0.9162

i)

P(630000<X<720000) = P(-1.25<z<1.38) = 0.8106

j)

The number of houses were sold between \$630,000 and \$720,000 is 35 * 0.8106 = 28.371