The mean production of cows is normally distributed with a mean of 31 liters, and standard deviation of 5.9 liters. What is the probability that daily production is between 31.1 and 38.9 liters?

Answer 1

x = daily production

want to find P(31.1 < x < 38.9) when mean is normally distributed with men 31 and std dev 5.9

need to convert above inequality to standardized normal (mean 0 std dev 1) so can use standardized normal probability table

z = (x - mean)/std dev

P ((31.1 - 31) /5.9 < z (38.9 - 31.1)/5.9))

Simplify then use std normal probability table to find probability. Note that P(a < z < b) = P(b) - P(a)