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.
To understand how to compute the probability for a given value in a standard normal distribution, we can follow these steps:
1. Understand the standard normal distribution: The standard normal distribution, also known as the Z-distribution, is a probability distribution with a mean of 0 and a standard deviation of 1. It is denoted by the letter Z.
2. Convert the given value to a Z-score: To compute probabilities in a standard normal distribution, we first need to convert the given value to a Z-score using the formula:
Z = (x - μ) / σ
Where:
Z is the Z-score,
x is the given value,
μ is the mean of the distribution,
σ is the standard deviation of the distribution.
3. Look up the Z-score in the standard normal distribution table: Once we have the Z-score, we can refer to a standard normal distribution table (also known as a Z-table or a standard normal table) to find the corresponding probability. The table provides the area under the curve to the left of the given Z-score.
4. Interpret the Z-table value: The value obtained from the Z-table represents the probability that a random variable from a standard normal distribution is less than the given Z-score. If we want to find the probability that Z is less than -0.13 (p(Z < -0.13)), we need to find the corresponding value in the table.
In this case, looking up -0.13 in the Z-table, we find that the area to the left of -0.13 is 0.4483. This means that 44.83% of the data falls to the left of -0.13 in the standard normal distribution.
So, p(Z < -0.13) = 0.4483 or 44.83%.
Remember that the Z-table provides probabilities for Z-values to the left of the given value. If you need the probability for a Z-value to the right (e.g., p(Z > -0.13)), you can calculate it by subtracting the value obtained from the table from 1.
I hope this explanation helps! Let me know if you have any further questions.