1. The weekly production of a corn farm can be modeled with a normal random vari

Question

1. The weekly production of a corn farm can be modeled with a normal random variable that has a mean of 8 tons and a variance of 4 tons. Use the values in (i)-(iii) to answer the questions below i (0.75) 0.773, (1.5) 0.933, (-1) = 0.159, (-0.125) 0.450, = = = D(-0.25) 0.401, (0.5)-0.309, (0.35) = 0.637. ii -1 (0.972) = 1.917. "(0.740) = 0.643. -1(0.95) 1.645 111 Zo.65 =0.385, 20.35 = 0.385, 20.175 = 0.935, 20.325 = 0.453. (a) What is the probability that, in a given week, production is greater than 11 (b) What is the probability that, in a given week, production is between 6 and 7.5 tons? (e) How many tons represents the 35th percentile in weekdly production?

Explanation / Answer

We have, the z- values and corresponding probabilities associated with it

Mean is 8, Variance is 4 which implies standard deviation is 2, as Variance= (Standard deviation)^2

        Z= (11-8)/2=>z=1.5, So basically probability that z is greater than 1 tonne would be 1-phi(1.5), as phi(1.5) means the cumulative probability that z can be upto 1.5 or equivalently production can be up to 11 tonne =>1-phi(1.5)= 1-.933 =.067

(b)Probability that in a given week production is between 6 to 7.5 tonne. Let’s calculate z values first.

Z1= (7.5-8)/2=-.25,                                 Z2=(6-8)/2=-1

So, basically the probability is phi(-.25)- phi(-1), which is .401-.159 =.242

This means (x-8)/2= (-.385)

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