Math 227 - Statistics » Spring 2023 » 11KC Sampling Distributions and Estimators & The Central Limit Theorem

Need help with your exam preparation?

Question #1
Consider rolling a single, fair, six-sided dice. Find the probability distribution, mean, variance, and proportion of odds. What is the mean? (Round to the nearest ten-thousandth.)
A.   2.5
B.   3.5
C.   3.9
D.   4.5
Question #2
Consider rolling a single, fair, six-sided dice. Find the probability distribution, mean, variance, and proportion of odds. What is the variance? (Round to the nearest ten-thousandth.)
A.   2.1144
B.   3.1247
C.   2.9167
D.   2.6193
Question #3
Consider rolling a single, fair, six-sided dice. Find the probability distribution, mean, variance, and proportion of odds. What is the proportion of odds? (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.5
B.   0.3
C.   0.8
D.   0.9
Question #4
Roll a dice five times. Record the results in Sample 1. Repeat the experiment for Sample 2, 3, and 4. In a live classroom setting, actual survey data is used. In this knowledge check online environment, please use the following data: Sample 1 Sample 2 Sample 3 Sample 4 2 4 1 6 2 1 5 4 3 5 5 1 5 5 3 3 4 6 4 4 Calculate the sample means, sample variances, the sample proportions of odds, the mean of the distribution of sample means, the mean of the distribution of sample variances, and the mean of the distribution of sample proportions of odds. Compare the means of the distributions of sample statistics to the population parameters. What is the the mean of the distribution of sample means? (Round to the nearest ten-thousandth.)
A.   3.15
B.   3.65
C.   2.95
D.   3.55
Question #5
Roll a dice five times. Record the results in Sample 1. Repeat the experiment for Sample 2, 3, and 4. In a live classroom setting, actual survey data is used. In this knowledge check online environment, please use the following data: Sample 1 Sample 2 Sample 3 Sample 4 2 4 1 6 2 1 5 4 3 5 5 1 5 5 3 3 4 6 4 4 Calculate the sample means, sample variances, the sample proportions of odds, the mean of the distribution of sample means, the mean of the distribution of sample variances, and the mean of the distribution of sample proportions of odds. Compare the means of the distributions of sample statistics to the population parameters. What is the the mean of the distribution of sample variances? (Round to the nearest ten-thousandth.)
A.   2.195
B.   2.773
C.   2.875
D.   3.128
Question #6
Roll a dice five times. Record the results in Sample 1. Repeat the experiment for Sample 2, 3, and 4. In a live classroom setting, actual survey data is used. In this knowledge check online environment, please use the following data: Sample 1 Sample 2 Sample 3 Sample 4 2 4 1 6 2 1 5 4 3 5 5 1 5 5 3 3 4 6 4 4 Calculate the sample means, sample variances, the sample proportions of odds, the mean of the distribution of sample means, the mean of the distribution of sample variances, and the mean of the distribution of sample proportions of odds. Compare the means of the distributions of sample statistics to the population parameters. What is the the mean of the distribution of sample proportions of odds? (Round to the nearest ten-thousandth.)
A.   0.55
B.   0.29
C.   0.44
D.   0.35
Question #7
An elevator’s maximum capacity is 16 passengers or a total weight of 2500 lb. Male weights are normally distributed with a mean of 189 lb. and a standard deviation of 39 lb. Find the probability that 1 randomly selected male has a weight greater than 156.25 lb. (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.7114
B.   0.7226
C.   0.8192
D.   0.7995
Question #8
An elevator’s maximum capacity is 16 passengers or a total weight of 2500 lb. Male weights are normally distributed with a mean of 189 lb. and a standard deviation of 39 lb. Find the probability that a sample of 16 males have a mean weight greater than 156.25 lb. (which exceeds the maximum capacity). (Express your answer as a decimal rounded to the nearest ten-thousandth.)
A.   0.9884
B.   0.9996
C.   0.9112
D.   0.8569

Need help with your exam preparation?