You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of G = 4.Your sample, which is Sample 1 in the table below, has a mean of x = 89.1. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)(a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidenceinterval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)• Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.• For the points (and ◆), enter the population mean, μ = 90.85.0H+++85.080% confidence interval91.0५ |80% 80% 95% 95%lower upper lower upperlimit limit limit limit?S1 89.1???S2 90.7 89.2S3 89.8 88.3S4 91.9 90.492.2 88.4 93.091.3 87.5 92.193.4 89.6 94.2S5 89.4 87.990.9 87.1 91.7S6 90.8 89.3 92.3 88.5 93.1S7 90.6 89.192.1 88.3 92.994.2 90.4 95.0S8 92.7 91.2S9 88.9 87.4S10 90.5| 89.0S11 91.9 90.490.4 86.6 91.292.0 88.2 92.893.489.6 94.2S12 91.0 89.592.5 88.7 93.3S13 91.1 89.6 92.6 88.8 93.4S14 90.9 89.492.4 88.6 93.2S15 89.2| 87.7 90.7 86.9 91.5S16 90.2 88.791.7 87.9 92.5S17 87.3 85.888.8 85.0 89.6S18 89.9 88.4 91.4 87.6 92.2S19 89.9 88.491.4 87.6 92.2S20 89.0 87.5 90.5 86.7 91.397.085.097.085.0HH85.095% confidence interval80% confidence intervals(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n = 12 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.91.097.0 85.097.0HHH95% confidence intervals97.097.0 18(c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the20correct statement.When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible thatmore or fewer than 95% of the samples will contain the population mean.(d) Choose ALL that are true.If there were a Sample 21 of size n=24 taken from the same population as Sample 14, then the 95% confidenceinterval for Sample 21 would be narrower than the 95% confidence interval for Sample 14.The 80% confidence interval for Sample 14 is narrower than the 95% confidence interval for Sample 14. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.From the 95% confidence interval for Sample 14, we cannot say that there is a 95% probability that thepopulation mean is between 88.6 and 93.2.The 80% confidence interval for Sample 14 does not indicate that 80% of the Sample 14 data values are between89.4 and 92.4.None of the choices above are true.

Question

You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of G = 4.Your sample, which is Sample 1 in the table below, has a mean of x = 89.1. (In the table, Sample 1 is written &#34;S1&#34;, Sample 2 is written &#34;S2&#34;, etc.)(a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidenceinterval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)• Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.• For the points (and ◆), enter the population mean, μ = 90.85.0H+++85.080% confidence interval91.0५ |80% 80% 95% 95%lower upper lower upperlimit limit limit limit?S1 89.1???S2 90.7 89.2S3 89.8 88.3S4 91.9 90.492.2 88.4 93.091.3 87.5 92.193.4 89.6 94.2S5 89.4 87.990.9 87.1 91.7S6 90.8 89.3 92.3 88.5 93.1S7 90.6 89.192.1 88.3 92.994.2 90.4 95.0S8 92.7 91.2S9 88.9 87.4S10 90.5| 89.0S11 91.9 90.490.4 86.6 91.292.0 88.2 92.893.489.6 94.2S12 91.0 89.592.5 88.7 93.3S13 91.1 89.6 92.6 88.8 93.4S14 90.9 89.492.4 88.6 93.2S15 89.2| 87.7 90.7 86.9 91.5S16 90.2 88.791.7 87.9 92.5S17 87.3 85.888.8 85.0 89.6S18 89.9 88.4 91.4 87.6 92.2S19 89.9 88.491.4 87.6 92.2S20 89.0 87.5 90.5 86.7 91.397.085.097.085.0HH85.095% confidence interval80% confidence intervals(b) Press the &#34;Generate Samples&#34; button below to simulate taking 19 more samples of size n = 12 from the population. Notice that the confidenceintervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.91.097.0 85.097.0HHH95% confidence intervals97.097.0 18(c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the20correct statement.When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% ofthe samples will contain the population mean.When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible thatmore or fewer than 95% of the samples will contain the population mean.(d) Choose ALL that are true.If there were a Sample 21 of size n=24 taken from the same population as Sample 14, then the 95% confidenceinterval for Sample 21 would be narrower than the 95% confidence interval for Sample 14.The 80% confidence interval for Sample 14 is narrower than the 95% confidence interval for Sample 14. This iscoincidence; when constructing a confidence interval for a sample, there is no relationship between the level ofconfidence and the width of the interval.From the 95% confidence interval for Sample 14, we cannot say that there is a 95% probability that thepopulation mean is between 88.6 and 93.2.The 80% confidence interval for Sample 14 does not indicate that 80% of the Sample 14 data values are between89.4 and 92.4.None of the choices above are true.

Accepted Answer

The question is about confidence interval.Given :Mean of the population (  ) = 90Standard deviation…