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 compute the probability p(z < -0.13) for a standard normal distribution, you can follow these steps:
1. Understand the standard normal distribution: The standard normal distribution, also known as the z-distribution or the Gaussian distribution, has a mean of 0 and a standard deviation of 1. It is a symmetrical bell-shaped curve.
2. Use a z-table: A z-table is a table that provides the cumulative probability values corresponding to different z-scores. The z-score represents the number of standard deviations a value is from the mean.
3. Standardize the value: To use the z-table, you need to standardize the given value (-0.13) by converting it into a z-score. The formula to standardize a value is:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
In this case, since it is a standard normal distribution, the mean (μ) is 0, and the standard deviation (σ) is 1.
z = (-0.13 - 0) / 1 = -0.13
4. Locate the z-score in the z-table: Once you have the z-score (-0.13), locate it in the z-table. The z-table provides the cumulative probability up to the given z-score. The table is divided into positive z-scores, so to find the probability for a negative z-score, you need to consider the area under the curve to the left of the z-score.
In the table, find the row corresponding to the tenths digit of the z-score (-0.1) and the column corresponding to the hundredths digit (0.03). The value in the table where these row and column intersect gives the cumulative probability.
For -0.1 row and 0.03 column, the cumulative probability value in the table is approximately 0.4483.
5. Interpret the result: The cumulative probability value obtained from the z-table represents the probability of getting a z-score less than -0.13 in a standard normal distribution. In this case, p(z < -0.13) is approximately 0.4483, which means there is a 44.83% chance of getting a value less than -0.13 in a standard normal distribution.
Note: Some variations may exist among different z-tables, so it's essential to use a reliable and accurate table or calculator when performing such calculations.