Question

given that is a standard normal random variable, compute the following probabilities. round your answers to 4 decimal places.

Answer 1

To calculate the probabilities in this question, use the standard normal distribution and the Z-score formula. The Z-score is the number of standard deviations an observation or value is from the mean. Use a Z-table or a calculator to find the probabilities.

Step-by-step explanation:

To calculate the probabilities in this question, we need to use the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. We can use the Z-score formula to find the probabilities. The Z-score is the number of standard deviations an observation or value is from the mean.

1. To find the probability of a Z-score less than a given value, we can use a Z-table or a calculator. The area under the curve to the left of the Z-score represents the probability. For example, if we want to find the probability of a Z-score less than 1.5, we look up 1.5 in the Z-table and find the corresponding area or probability.
2. To find the probability of a Z-score greater than a given value, we can subtract the probability of a Z-score less than that value from 1. For example, if we want to find the probability of a Z-score greater than 2.2, we first find the probability of a Z-score less than 2.2 and then subtract it from 1.
3. To find the probability between two Z-scores, we subtract the probability of the lower Z-score from the probability of the higher Z-score. For example, if we want to find the probability between a Z-score of -1.5 and 1.5, we find the probability of a Z-score less than 1.5 and subtract the probability of a Z-score less than -1.5 from it.