Question

The mean yield for one acre plot is 662 kg with a S.D. 32 kg. assuming normal distribution , how
many one acre plot in a batch of 1000 plots would you expect to have yield
1. Over 700 kg
2. Below 650 kg

Answer 1

Answer:

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Explanation:

mean(m) = 662 kg

sd = 32 kg

for x=600 kg, z =

$\frac{600-662}{32}=-1.9375$

for x=750 kg, z = 

$= \frac {750-662}{32} =2.75$

Using Z table:

P(z < -1.9375) = 0.0268

P(z < 2.75) = 0.9970

P(-1.9375 < z < 2.75) = 0.9970 - 0.0268 = 0.9702

So probability of a land with yield between 600 kg and 750 kg is 0.9702

total plots = 1000

Number of plots with expected yield between 600 and 750 kg is given by

N = 1000×0.9702 = 970.2 ≈ 970

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