.The mean yield for one acre plot is 662 kg with a s.d 32kg .assuming normal distribution how many one acre plot in a batch of 1000 plots would your expect to have yield between 600 and 750 kg.
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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 ) = P (X <= x)
Probability p of yield x being in the range 600kg and 750kg = P(600 ≤ x ≤ 750)
p = P[ (600 - 662)/32 ≤ X ≤ (750 - 662)/32 ]
= P [ -1.9375 ≤ X ≤ 2.75 ]
= P( X ≤ 2.75) - [ 1 - F( X ≤ 1.9375) ]
=> p = F (2.75) + F (1.9375) - 1
Look up these values in normal distribution function tables. I have the two values as below:
p = 0.997 + 0.973 - 1 = 0.97 approximately.
You need to know how to read and interpret the values in the table.
0.97 : 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, that are likely to produce yield in the given range
= N * p
= 1000 * 0.97 = 970 plots.
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 ) = P (X <= x)
Probability p of yield x being in the range 600kg and 750kg = P(600 ≤ x ≤ 750)
p = P[ (600 - 662)/32 ≤ X ≤ (750 - 662)/32 ]
= P [ -1.9375 ≤ X ≤ 2.75 ]
= P( X ≤ 2.75) - [ 1 - F( X ≤ 1.9375) ]
=> p = F (2.75) + F (1.9375) - 1
Look up these values in normal distribution function tables. I have the two values as below:
p = 0.997 + 0.973 - 1 = 0.97 approximately.
You need to know how to read and interpret the values in the table.
0.97 : 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, that are likely to produce yield in the given range
= N * p
= 1000 * 0.97 = 970 plots.
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