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Yield for one acre plot = random variable x μ = mean of the distribution for yield = E (X) = 662 kg standard deviation = σ = 32 kg

Normal distribution variable = X = (x - μ)/σ cumulative probability function of the normal distribution: F(X)

Probability p of yield x being in the range 600 kg and 750 kg = F(600 ≤ x ≤ 750) p = F[ (600 - 662)/32 ≤ X ≤ (750 - 662)/32 ] = F [ -1.9375 ≤ X ≤ 2.75 ] = F( X ≤ 2.75) - [ 1 - F( X ≤ 1.9375) ] p = F (X ≤ 2.75) + F ( X ≤ 1.9375) - 1

Look up these values in a standard normal distribution function tables. p = 0.997 + 0.973 - 1 = 0.97 approximately.

This is the probability with which a randomly selected plot may produce a yield in the given range.

Number of plots we have = N = 1000 plots = data sample size.

Number of plots which are likely to produce yield in the given range = N * p = 1000 * 0.97 = 970 plots.