Question

Many farmers use the height of their corn on July 4th as an indication of the entire crop. In a random sample of corn-stalk heights on July 4th in Columbia County, x⎯⎯⎯x = 25.6, s = 0.9 inch, and a histogram of the observations was bell-shaped.

Fill in the blank. (Give your answer to two decimal places.)

The approximate proportion of observations that lies between 23.8 and 27.4 is __

Answer 1

0.9544

Explanation:

Given that, his bell shapes and hence follows a normal distribution.

Mean (x) = 25.6 ; standard deviation (s) = 0.9

Approximate proportion of observation that lies between 23.8 and 27.4

Taking the Zscores of both values :

X - mean / standard deviation

(23.8 - 25. 6) / 0.9 = - 1.8/0.9 = - 2

P(Z < - 2) = 0.0228

Also;

(27.4 - 25.6) / 0.9 = 1.8 / 0.9 = 2

P(Z> 2) = 0.9772

0.9772 - 0.0228 = 0.9544