Question

given that is a standard normal random variable, compute the following probabilities. round your answers to 4 decimal places. p(z >= -0.50)

Answer 1

To calculate P(Z >= -0.50), find the area to the left of z = -0.50 using a z-table or calculator, which is 0.3085, and subtract from 1 to get the answer 0.6915.

Step-by-step explanation:

The probability P(Z >= -0.50) represents the area under the standard normal curve to the right of the z-score -0.50. To find this, we refer to a z-table, or use a calculator with statistical functions. The z-table shows that the area to the left of z = -0.50 is 0.3085. Since a standard normal distribution is symmetrical, we subtract this from 1 to get the area to the right.

Therefore, P(Z >= -0.50) = 1 - P(Z < -0.50) = 1 - 0.3085 = 0.6915.

This calculation is essential in statistics, especially when performing hypothesis testing or finding confidence intervals in a normally distributed dataset.