C. When n = 100, 𝜇 = 1 and a standard deviation of 𝜎 = 1, what is the chance a sample mean from the sampling distributio

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C. When n = 100, 𝜇 = 1 and a standard deviationof 𝜎 = 1, what is the chance a sample mean from thesampling distribution is between 0.8 and 1.2?
Approximately 68%
Approximately 95%
Impossible to know
Approximately 99.7%

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Population Distribution Choose the population shape. Recall, the shape of the population is what determines how large of a sample size is needed for the sampling distribution to be Normal by the CLT. O Normal Uniform Skewed Categorical Population Parameters Select parameters for population distribution. Note these might not be the exact same as the simulated population values. a 50 10 Sample Size Select the sample size. The sample size helps determine the shape of the Sampling Distribution and it's variability. Choose different values to see the effect of the sample size on both the Sampled and Sampling Distribution. 2 2 10 4 7 13 24 45 83 155 288 1000 537 1000 # of Random Samples of size n Select number of times to; take a random sample, calculate the mean, and plot it. The 'real' Sampling Distribution will have all possible unique samples, N choose n to be exact, simulating this samples is not necessary. 10000 will do the trick! 1 10 10000
Frequency 900- 600- 300- 0- 25 I 50 Population Mean Population Standard Deviation X 49.91 10.05 75 100 will look more like the population distribution! Frequency 2.0- 1.5- 1.0 0.5- 0.0- 40 45 X 50 Sample Mean Sample Standard Deviation 5.9 45.94 55 60 estimating parameters. Frequency 900- 600- 300- 0- 40 45 -5X 55 Distribution of Means Average 49.88 Distribution of Means Std Dev'n 3.18 60
Using the app. Click Skewed under Population Distribution Inputs. Under Population Parameters, select a mean of = 1 and a standard deviation of 1 Slide the Sample size slider to 5. Set the simulation to randomly sample 10000 samples of 5. Based on the Central Limit Theorem, if n is sufficiently large, the Sampling Distribution of the sample mean should be approximately Normal and have a mean of and standard deviation of ✓n A. Is the sample size large enough so that sampling distribution approximately Normal? O Yes, even though the sample size in only 5 the sampling distribution looks approximately Normal. No, when the population is highly skewed, n = 5 is not large enough for sampling distribution to be Normal. Using the app. Slide the Sample size slider from 5 to 100. Keep other inputs the same. B. When n 100, is the sample size large enough so that sampling distribution approximately Normal? Yes, by increasing the sample size the sampling distribution looks approximately Normal. O No, increasing the sample size does not make the sampling distribution become more Normal. C. When n = 100,- 1 and a standard deviation of o1, what is the chance a sample mean from the sampling distribution is between 0.8 and 1.2? O Approximately 68% O Approximately 95% O Impossible to know O Approximately 99.7% Submit Answer