U.S. Bureau of the Census data reveal the largest town in the State of KS has a

Question

U.S. Bureau of the Census data reveal the largest town in the State of KS has a population of one million families. The data show that acreage owned per family is normally distributed with a mean of 10.0 acres and a standard deviation of 1.5 acres. Calculate the following:

The percentage of families that own at least 8.1 acres.

The number of families that own at least 8.1 acres.

The percentage of families that own between 7.0 and 8.1 acres.

The minimum acreage owned by the 5% of families owning the largest amount of acreage.

Explanation / Answer

mean = 10 , sd = 1.5

Z =(X - 10)/1.5

a)P(X > 8.1)

= P(Z> ( 8.1 - 10)/1.5)

= P(Z> -1.26666666667)

= 0.8974

hence9.74%

b)

1 million *0.8974

= 0.8974 million

c)

P(7 <X< 8.1)

= P ( 2<Z<1.27 )

=0.0792

d)

P(Z >z*) = 0.05

z* = 1.645

X* = 10 +1.645 * 1.5

= 12.4675

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