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 your expect to have yield between 600 and
750 kg.

Answer 1

mean yield = m = 662 kg
standard deviation = 32 kg

for x=600 kg
z = 600 - 662/32 = -1.9375

for x=750 kg
z = 750-662/32 = 2.75

Using Z table we get the values;
= 0.0268 and 0.9970
so, 

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

Therefore, the probability of land between 600-750 kg =0.9702

number of total plots = 1000

Number of plots with expected yield= N = 1000×0.9702 = 970.2