Ok so I am having difficulty understand the concept behind standard normal distribution probabilities, in the questions I am getting a graph and a table FILLED with numbers, top header column has values from 0.01 to 0.09 and on left I have 0.0 to 3.8!
and the questions are like :
i) P(Z<1.5)=
etc.
Now I do not get what they mean by calculating the area at the bottom of the curve (NOT sure what the curve represents!) to the left, so please when explaining use an example and use simple terminology
Best Answer
You're right in wanting to understand the concept first before you start trying to calculate things.
The standard normal distribution is a probability distribution given by the density $f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$ for $-\infty < x < \infty$ (this is the "curve" they are talking about). It has many applications which you will find out about, and many interesting properties. Its mean is $0$ and its standard deviation is $1$.
The one thing it does not have is a nice formula for calculating probabilities. That is where the table comes in.
The table gives you (to a certain number of decimal places) the cumulative distribution function $F(x)$, which is the probability that a standard normal random variable is less than or equal to $x$, for values of $x$ from $0.0$ to $3.89$ in steps of $0.01$. For example, to look up $P(Z \le 2.34) = F(2.34)$, you look in the row labelled $2.3$ under the column heading $0.04$, and you should find $.9904$.