Question

1. A local agriculture producer had a wheat yield last year of 72 bushels per acre. The producer had an unusually productive year. The normal wheat yield on this particular farm is 38 bushels per acre with a variance (σ²) of 16 bushels per acre.

1. What is the probability that the wheat yield this year will be within one standard deviation (±) of the mean? Hint: think Empirical Rule.

Answer 1

Let X be the weight yield

with mean , = 38

and standard deviation , = 16

From Empirical rule we know that 68% of the observation lie within one standard deviation of the mean

That is ,

which implies P( 38-16 < X < 38+16) =0.68

that is , P( 22 < X < 54) = 0.68

Therefore , probability that the wheat yield this year will be within one standard deviation of the mean( within 22 to 54) is 0.68 or 68%

Answer : 68% or 0.68

Note :

From Empirical rule we know that 68% of the observation lie within one standard deviation of the mean

That is ,

95% of the observation lie within two standard deviation of the mean

That is ,

99.7% of the observation lie within three standard deviation of the mean

That is ,