mean is 4200 a day standard deviation is 720 a day

Question

low is less than 2500 high is more than 6000 what percent of days will be high what percent will be low

Answer 1

For low we need to calculate the Z-score, Z_L=(2500-4200)/720=-2.361 approx.

For high we need Z_H=(6000-4200)/720=2.500.

This means that the low of 2500 is 2.361 standard deviations below the mean and 6000 is 2.5 standard deviations above the mean. Using tables we get:

N(Z_L)=0.009 or 0.9%, N(Z_H)=0.994 or 99.4%.

In other words, there is a 0.9% probability of lower than 2500; and a 99.4% probability of lower than 6000. But we want to know the probability of higher than 6000, so this is 100-99.4=0.6%.