Let's shake on it: A random sample of 12-ounce milkshakes from 11 fast-food restaurants had the following number of calories.375 608 473 476 504 510 472700 642 591 580 Send data to ExcelAssume the population standard deviation is =σ85.Part 1 of 3(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.It is necessary to check whether the population is approximately normal because ▼the sample size is less than or equal to 30.Part 2 of 3(b) Following is a dotplot of these data. Is it reasonable to assume that the population is approximately normal?350400450500550600650700It ▼is reasonable to assume that the population is approximately normal.Part: 2 / 32 of 3 Parts CompletePart 3 of 3(c) If appropriate, construct an 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants. Round the answers to at least two decimal places.An 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants is <<μ.

(c) If appropriate, construct an 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants. Round the answers to at least two decimal places.An 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants is <<μ.

A sample of size =n92 is drawn from a normal population whose standard deviation is =σ5.1. The sample mean is =x35.33.Part 1 of 2(a) Construct a 99.9% confidence interval for μ. Round the answer to at least two decimal places.A 99.9% confidence interval for the mean is 33.58<<μ37.08.Part: 1 / 21 of 2 Parts CompletePart 2 of 2(b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain.The confidence interval constructed in part (a) ▼(Choose one) be valid since the sample size ▼(Choose one) larg

A sample of size =n90 is drawn from a normal population whose standard deviation is =σ9.7. The sample mean is =x38.78.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Construct an 80% confidence interval for μ. Round the answer to at least two decimal places.An 80% confidence interval for the mean is <<μ.

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of =σ5. We have taken a random sample of size =n10 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is =x101.1. Also shown are the lower and upper limits of the 75% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 90% confidence interval. Suppose that the true mean of the population is =μ100, which is shown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size =n10 from this same population. (The 75% and 90% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.x 75%lowerlimit 75%upperlimit 90%lowerlimit 90%upperlimitS1 101.1 99.3 102.9 98.5 103.7S2 Generate SamplesS3S4S5S6S7S8S9S10S11S12S13S14S15S16S17S18S19S2075% confidence intervals94.0106.090% confidence intervals94.0106.0(a)How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, =μ100? (b)How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, =μ100? (c)Choose ALL that are true. For each sample, the 75% confidence interval for the sample is included in the 90% confidence interval for the sample. It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. The sample means for Sample 19 and Sample 20 are different, so the center of the 90% confidence interval for Sample 19 is different from the center of the 90% confidence interval for Sample 20. We would expect to find more 75% confidence intervals that contain the population mean than 90% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval. None of the choices above are true.

Stock prices: The Standard and Poor's (S&P) 500 is a group of 500 large companies traded on the New York Stock Exchange. Following are prices, in dollars, for one day for a random sample of eight stocks.53.55 84.25 201.94 24.68 53.4784.86 8.11 74.23 Send data to ExcelAssume the population standard deviation is =σ54.Part: 0 / 20 of 2 Parts CompletePart 1 of 2(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.It is necessary to check whether the population is approximately normal because ▼(Choose one).