The mean value of a land and building per acre from a sample of a farm is $1500, with a standard deviation of $200. What is the percentage of farms whose land and building values acre are between $1300 and $1700?

Solution:

Given,

The mean value of a land and building per acre from a sample of a farm = $1500.(μ)

Standard deviation = $200.(σ)

The data has normal distribution,

Using z = x - μ/σ

For x = 1300

Z = (1300 - 1500)/200 = -1

For x = 1700

Z = (1700 - 1500)/200 = 1

Using standard normal z- value table,

P - value = P(-1 < z < 1) = 1- 2P (z > |1|)

Substituting the values

= 1- 2(0.1586553)

= 0.6826894 ≈ 0.6827

Therefore, the percentage is 68.27%

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The mean value of a land and building per acre from a sample of a farm is $1500, with a standard deviation of $200. What is the percentage of farms whose land and building values acre are between $1300 and $1700?

Summary:

The mean value of a land and building per acre from a sample of a farm is $1500, with a standard deviation of $200.The percentage of farms whose land and building values are between $1300 and $1700 is 68.27%.