Question

The average time it takes a loaf of bread to rise is 2.4 hours with a standard deviation of 0.6. what is the z-score of a loaf that takes 3.6 hours to rise?

Answer 1

Formally we are looking to the following probability:

`P(X < 3.6)`
Do the following operations:

`P(X< 3.6)=P(X-2.4< 3.6-2.4)\\=P((X-2.4)/(0.6)< (3.6-2.4)/(0.6))\\=P(N(0,1)< 2)`
Using the table of the normal law, we get the following value:

`P(X < 3.6)=0.97`

Answer 2

A z-score is defined as the difference between one observation and the mean (average) of all observations, divided by the standard deviation. Here, the difference is: 3.6 minus 2.4 = 1.2. The standard deviation is 0.6, so 1.2 divided by 0.6 = 2.0.