Find the z-score for the standard normal distribution where:
P(z< -a) = 0.2451
I don't know what you mean by "-a."
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.2451) and its Z score.
To find the z-score for the given probability, we need to find the value of "a" such that P(z < -a) = 0.2451.
Since the standard normal distribution is symmetrical, we can use the z-table to find the z-score related to the given probability.
The z-table provides the probability of the standard normal distribution up to a given z-score. In this case, we are given the probability to the left of -a.
Looking up the value 0.2451 in the z-table, we find that the closest z-score is approximately -0.705.
Therefore, the z-score for P(z < -a) = 0.2451 is approximately -0.705.
To find the z-score for the standard normal distribution where P(z < -a) = 0.2451, you can use a standard normal distribution table or a statistical software.
Here's how you can use a standard normal distribution table:
1. Look up the probability value of 0.2451 in the standard normal distribution table. This value corresponds to the area under the curve to the left of the z-score.
2. Find the closest probability value in the table that is less than or equal to 0.2451. Let's say that the closest value corresponds to a z-score of -a'.
3. Take the absolute value of -a' to find the z-score for the standard normal distribution. This is because the z-score represents the number of standard deviations away from the mean, and we want to know the distance from the mean in a negative direction.
For example, if the closest probability value in the table is 0.2578, then -a' would be -0.2578. Therefore, the z-score would be 0.2578.
Alternatively, you can use a statistical software or calculator to calculate the z-score directly. Most statistical software packages have built-in functions that can calculate the z-score given a probability value.
Remember that the standard normal distribution is symmetric, so if P(z < -a) = 0.2451, then P(z > a) = 0.2451 as well.