# if z-value is a negative number, how can i calculate the Probability?

#### katte

##### New Member
Hello guys, I have an important question I want to ask. I have already searched the web and my statistics book but I can not find the answer I stumbled across this problem when preparing for my final from statistics and I can not figure out how we can get P=1 from a z-value=-10.6066...? Can somebody please explain? There is also another problem following the same directions just with the change that its want the probability that its mean will be less than 970. There, the z-value turned out to be -13.59 and the P=0. My teacher checked this both answers as correct so I am very confused as to when a negative z-value equals 0 and when 1.

In a normal PD, the mean equals 1100 and the standard deviation equals 80.

If you choose a sample of size 50 from the original population, what is the probability that its mean will be more than 980?

z=(980-1100)/(80/√50)=(-120)/11,3137085=-10,60660172=-10,6066
P=1

If I choose a sample of size 50 from the original population the probability that its mean will be more than 980 is nearly certain.

Thank you so much for your help,

Kate

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Without looking at your question I will provide some basic information. Negative values are on the left side tail, below the mean. A probabilility of 0 is likely just rounded down to zero. If you think that -1.96 is = 0.025 then even smaller value will be even closer to 0.

#### bruin

##### Member
The probability/area under the curve in a normal distribution is not ever 0 or 1. However, with such large negative z-scores as -10.6 and -13.59, the probabilities can be darn close to 0 or 1.

The difference between the two problems is whether you are finding the body or the tail.

With a negative z-score, to the left (below) is the tail, and to the right (above) is the body. (With a positive z-score this is flipped).

With such LARGE negative z-scores, the area in the tail will be close to 0 and the area in the body will be close to 1.