In an agricultural experiment, a large uniform field was planted with a single v

Question

In an agricultural experiment, a large uniform field was planted with a single variety of

wheat. The field was divided into many plots and the yield (lb.) of grain was measured for each

plot. These plot yields followed approximately a normal distribution with mean 88 lb. and

standard deviation 7 lb.

(a) The probability of a plot yield is 80 lb. or less is _________________

(b) The probability of a plot yield is between 75 and 90 lb. _________________

(c) If the yield is between 75 and 90lbs, the probability of a plot yield is 80lb. or less

is______________________.

Explanation / Answer

as we know that z score =(X-mean)/std deviation

a)P(X<80)=P(Z<(80-88)/7)=P(Z<-1.1429)=0.1265

b)P(75<X<90)=P((75-88)/7<Z<(90-88)/7)=P(-1.8571<Z<0.2857)=0.6125-0.0316=0.5808

c) P(X<80|75<X<90) =P(75<X<80)/P(75<X<90)=(0.1265-0.0316)/0.5808=0.1634

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