Reference no: EM132412481

1. A population's distribution is normal with a mean of 18 and standard deviation of 4. A sample of 16 observations is selected and a sample mean computed. What is the probability that the sample mean is more than 20?
2. An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 minutes?
3. A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students study per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?
4. As the size of the sample increases, what happens to the shape of the distribution of sample means?