Question

The average collection period for loans outstanding is found to be 37 days with a population standard deviation of 12 days. A sample of 18 collection times were taken for a study. Use megastat to solve the following questions. Find the probability that the sample mean would be: Q1 more than 40 days Q2 less than 29 days Q3 between 35 and 45 days Q4 the top 16% of the times. Q5 the bottom 13% of the times Q6 the middle 99% of the times.

Answer 1

To solve these questions using the average collection period for loans outstanding, we need to use the Z-score formula and the Z-table. The Z-score formula is Z = (X - mu) / (sigma / sqrt(n)), where X is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Step-by-step explanation:

To solve these questions using the average collection period for loans outstanding, we will need to use the Z-score formula and the Z-table. The Z-score formula is Z = (X - mu) / (sigma / sqrt(n)), where X is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Q1: To find the probability that the sample mean is more than 40 days, we need to find the Z-score for 40 and use the Z-table to find the probability. Q2: To find the probability that the sample mean is less than 29 days, we need to find the Z-score for 29 and use the Z-table to find the probability. Q3: To find the probability that the sample mean is between 35 and 45 days, we need to find the Z-scores for both values and use the Z-table to find the probability. Q4: To find the top 16% of the times, we need to find the Z-score that corresponds to the 84th percentile. Q5: To find the bottom 13% of the times, we need to find the Z-score that corresponds to the 13th percentile. Q6: To find the middle 99% of the times, we need to find the Z-scores that correspond to the 0.5th and 99.5th percentiles.