Question 2, which is what I would like help with, is related to question 1. That

Question

Question 2, which is what I would like help with, is related to question 1. That is why both are posted

1. In an agricultural experiment, a large uniform field was planted with a single variety of wheat. The field was divided into many plots (each plot being 8 x 100 ft) 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. What percentage of the plot yields were a) 80 lb or less? b) 90 lb or less? c) 75 lb or more? d) between 90 and 100 lb? e) less than 75 or more than 90 lb? f) less than 75 or more than 80 lb? 2. For the wheat-yield distribution of in the previous question, find a) the cutoff for the largest 11% of yields b) the cutoff for the smallest 6% of yields c) 3rd quartile d) the 66th percentile

Explanation / Answer

2)a) P(X > x) = 0.11

or, P((X - mean)/sd > (x - 88)/7) = 0.11
or, P(Z > (x - 88)/7) = 0.11

or, P(Z < (x - 88)/7) = 0.89

or, (x - 88)/7 = 1.23

or, x = 1.23 * 7 + 88

or, x = 96.61

b) P(X < x) = 0.06

or, P((X - mean)/sd < (x - 88)/7) = 0.06
or, P(Z < (x - 88)/7) = 0.06

or, (x - 88)/7 = -1.56

or, x = -1.56 * 7 + 88

or, x = 77.08

c) P(X < x) = 0.75

or, P((X - mean)/sd < (x - 88)/7) = 0.75
or, P(Z < (x - 88)/7) = 0.75

or, (x - 88)/7 = 0.67

or, x = 0.67 * 7 + 88

or, x = 92.69

d) P(X < x) = 0.66

or, P((X - mean)/sd < (x - 88)/7) = 0.66
or, P(Z < (x - 88)/7) = 0.66

or, (x - 88)/7 = 0.41

or, x = 0.41 * 7 + 88

or, x = 90.87

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