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?
Formally we are looking to the following probability: [tex]P(X < 3.6)[/tex] Do the following operations: [tex]P(X< 3.6)=P(X-2.4< 3.6-2.4)\\=P(\frac{X-2.4}{0.6}< \frac{3.6-2.4}{0.6})\\=P(N(0,1)< 2)[/tex] Using the table of the normal law, we get the following value: [tex]P(X < 3.6)=0.97[/tex]
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.
