Question

Basic Computation: Finding Probabilities In Problems 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, and 50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.

Answer 1

To find the probabilities in these problems, use the standard normal distribution and calculate the z-score. Lookup the z-score in a z-table to find the corresponding probability and shade the area under the standard normal curve.

Step-by-step explanation:

To find the probabilities in these problems, we need to use the standard normal distribution and calculate the z-score. The z-score represents the number of standard deviations a value is from the mean. By looking up the z-score in a z-table, we can find the corresponding probability. It is important to note that the area under the normal curve to the left of the z-score is typically given in the z-table.

For example, in problem 84, we want to find the probability that the sum of a sample will be less than 5,000. We calculate the z-score for 5,000 using the formula (x - mean) / standard deviation. We then look up this z-score in the z-table to find the corresponding probability.

Follow this method for each problem, calculating the z-score and using the z-table to find the probability and shade the corresponding area under the standard normal curve.