Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).

a. P(z -1.5)


b. P(z -2.5)

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to each Z score.

To compute the probabilities P(z > -1.5) and P(z > -2.5), we need to use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a standard normal random variable is less than or equal to a given value.

a. P(z > -1.5):
To find this probability, we need to calculate 1 - P(z ≤ -1.5). We can use a table of the standard normal distribution or a statistical software to find the cumulative probability.

Using a standard normal table, we look up the value of -1.5, which corresponds to a cumulative probability of 0.0668. The table usually gives the probability for the left tail, so to find the probability in the right tail, we subtract this value from 1:

P(z > -1.5) = 1 - 0.0668 = 0.9332

So, the probability P(z > -1.5) is approximately 0.9332.

b. P(z > -2.5):
Similar to the previous question, we need to calculate 1 - P(z ≤ -2.5).

Using a standard normal table, we look up the value of -2.5, which corresponds to a cumulative probability of 0.0062. Again, we subtract this value from 1:

P(z > -2.5) = 1 - 0.0062 = 0.9938

So, the probability P(z > -2.5) is approximately 0.9938.