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ser-zykov [4K]
3 years ago
9

29. The mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $200. The data s

et has a bell-shaped distribution. Estimate the percent of farms whose land and building values per acre are between $1300 and $1700.
Mathematics
1 answer:
julia-pushkina [17]3 years ago
3 0

Answer: 68.27%

Step-by-step explanation:

Given : Mean value of land and buildings per acre from a sample of farms :

\mu=\$1500

\sigma= \$200

The data set has a bell-shaped distribution. i.e. it follows Normal distribution.

Using z=\dfrac{x-\mu}{\sigma} , for x= 1300 , we have

z=\dfrac{1300-1500}{200}=-1

For x= 1700 , z=\dfrac{1700-1500}{200}=1

Using standard normal z-value table,

P-value = P(-1<z<1)=1-2P(z>|1|)=1-2(0.1586553)=0.6826894\approx0.6827  [Round to nearest 4 decimal places.]

i.e. The percent of farms whose land and building values per acre are between $1300 and $1700 = 68.27%

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