A family is considering a move from a midwestern city to a city in california. The distribution of housing costs where the family currently lives is normal with mean $105,000 and standard deviation $18,200. The distribution of housing costs in the california city is normal with mean $235,000 and standard deviation $30,400. The family's current house is valued at $110,000.

A. 60.8 %

B. 87.52%

Explanation:

a. Calculation for what is the percentage of houses in the family's current city cost less than their home

Mean=μ=$105,000

Standard deviation =σ=$18,200

Given X=$110,000

P(X < $110,000) = P(Z < ($110,000 - $105,000) / $18,200)

=P(Z<($5,00O/$18,200)

= P(Z < 0.2747 )

Percentage = 0.608 *100

Percentage= 60.8 %

Therefore what the percentage of houses in the family's current city cost less than their home is 60.8%

b. Calculation for what percentage of houses there will cost more than theirs

California city

Mean=μ=$235,000

Standard deviation =σ=$30,400

P(X > $200,000) = P(Z > ($200,000 - Mean) / s)

= P(Z > ($200,000 - $235,000) / $30,400)

=P(Z > ($35,000/$30,400)

= P(Z > -1.1513)

Percentage= 0.8752 *100

Percentage= 87.52%

Therefore what percentage of houses there will cost more than theirs is 87.52%

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