# 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.

1
by nithyaBatra

2015-04-01T21:48:17+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.