I am having trouble understanding standard normal distribution such as if p(z<-0.13) the answer to that was 0.4483 but not understanding how that is computed.
It was determined by using calculus. Even If I could tell you exactly how, I doubt if you have the background to understand explanation.
To understand how to compute the probability of P(Z < -0.13) in the standard normal distribution, we need to use the standard normal table.
The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. It is often denoted as Z.
To find the probability P(Z < -0.13), we need to find the cumulative probability up to that value on the standard normal distribution.
Here are the steps to compute the probability:
1. Refer to a standard normal distribution table (also known as a z-table or a standard normal probability table).
2. Locate the row corresponding to the first digit(s) of your Z-score (in this case, -0.1). The rows are labeled with the first digit(s) of the Z-score in the table.
3. Locate the column corresponding to the second digit of your Z-score (in this case, 0.03). The columns represent the second decimal place of the Z-score in the table.
4. Find the corresponding value at the intersection of the row and column in the table. This value represents the cumulative probability up to that Z-score.
In this case, the value at the intersection of the row (-0.1) and the column (0.03) is 0.4483. This means that the probability of Z < -0.13 is approximately 0.4483 or 44.83%.
Remember, the values in the table represent the area under the curve of the standard normal distribution up to a certain Z-score. By referring to the table, you can find the probability associated with a specific Z-score or range of Z-scores.