1. If the standard deviation of the mean for the sampling distribution of random samples of size 36 from a large or infinite population is 2, how large must the sample size become if the standard deviation is to be reduced to 1.2?
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- it is known that the population standard deviation of weight among females is 30. assuming that we have a random sample of 210, what is the standard error of the average weight among women of a sample of this size?4. The time required for all cross-country skiers to complete a race has a normal distribution with a mean of 46 minutes and a standard deviation of 6 minutes. You choose a random sample of six skiers, and the mean of the sample is denoted i. What are the mean and standard deviation of ?A population is known to be normally distributed with standard deviation known to be 6.3. In order to test the hypothesis that the true value of the mean is 19 researchers collect a sample of size 36 and calculate the sample mean to be 16. State the distribution of the sample mean and then test this hypothesis using the appropriate test.
- 4. A normal population has the mean of 20 and the variance of 100. A random sample of size n = 69 is selected. (a) Find the standard deviation of the sample mean. (b) How large must the sample be if you want to halve the standard deviation of the sample mean?If x represents a random variable with mean 137 and standard deviation 16, then the standard deviation of the sampling distribution of the means with sample size 64 is 2. True O FalseConsider the distribution of the average number of hours that college students spend sleeping each weeknight. This distribution is very skewed to the right, with a mean of 5 and a standard deviation of 1. A researcher plans to take a simple random sample of 18 college students. If we were to imagine that we could take all possible random samples of size 18 from the population of college students, the sampling distribution of the average number of hours spent sleeping will have a shape that is ☐ Exactly normal. Just like the population (i.e., very skewed to the right). Less skewed than the population.
- 5. The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimcters. Assume the distributions of both types of breeds are normally distributed. (n) Suppose we are taking a random sample of 64 terriers. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 61 terriers excoedls 75 centimetcrs. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers excoeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.A dentist wants to estimate the average number of patients coming into her clinic each day. She estimates the standard deviation is 6 patients per day. If she wants to use a random sample of previous days for her sample, how many days should she include to be 95% sure her estimate is off by no more than 0.3 patients per day?Suppose we are about to sample 150 values from a normally distributed population that has a mean of 500 and a standard deviation of 10. What is the 80th percentile of the sampling distribution of the sample mean in this scenario? (Give your numeric response to at least 3 decimal places.
- What would be the mean of the sampling distribution of all possible sample means obtained from this population? If population with a positively skewed distribution of scores has a mean of 5 and a standard deviation of 4.Suppose we are about to sample 200 values from a normally distributed population that has a mean of 120 and a standard deviation of 70. What is the 10th percentile of the sampling distribution of the sample mean in this scenario? (Give your numeric response to at least 3 decimal places. Give only your numeric response, and no extra characters or symbols.)