Question

For a standard normal distribution, find: \[ P(z>-2.09) \] Express the probability as a decimal rounded to 4 decimal places.

Answer 1

We find P(z > -2.09) by subtracting the area to the left of z=-2.09 listed in the z-table from 1, resulting in a probability of 0.9817.

Step-by-step explanation:

To find the probability P(z > -2.09) for a standard normal distribution, we should use the z-table which gives us the area to the left of a given z-score. According to the z-table, the area to the left of z = -2.09 is approximately 0.0183. Since the total area under the standard normal curve equals 1, the area to the right of z = -2.09 is 1 - 0.0183, which equals 0.9817.

Thus, the probability P(z > -2.09) is:

1 - area to the left of z
= 1 - 0.0183
= 0.9817

Therefore, we have found the desired probability and it is 0.9817, rounded to four decimal places as requested.