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The central limit theorem looks at what specific values derived from a population? a. The variance of multiple samples O b. The median of multiple samples O c. The standard deviation of multiple samples O d. The average of multiple samplesWhich of the following is an implication of the central limit theorem? O a. The mean of the population can be approximated by the sum of the sample means. O b. The mean of the population can be approximated by the standard deviation of the sample means. O c. The mean of the population can be approximated by the square root of the sample means. O d. The mean of the population can be approximated by the mean of the sample means.In a sample of 250 households, the mean electric bill during January was $261. It is known that the population standard deviation is $25. Construct a 90% confidence interval for the population mean. O a. ($200, $345) O b. ($258, $264) O c. ($251, $271) O d. ($255, $263)A scientist is measuring the diameters of tree trunks. measuring twenty trees per tIip. If the scientist increases their sample size to thirty per trip. then what change should they expect to see in the means of the samples? D a. They will become uniformly distributed. D b. They will become more normally distributed. D c. They will become less normally distributed. '3' d. They will become logarithmically distributed. A biologist has a sample of lizards from a certain area. and their weights are normally distributed. If the biologist wants to expand the sample. but maintain its integrityr what should they do? 'u'il'hy? C} a. They should randomly choose lizards from the same area. because the data set only maintains its integrity if the new members of the sample come from a random sampling. D b. They should choose a mix of very light and very heavy lizards. because the data set only maintains its integrity if the mean remains the same. '3 c. They should randomly choose lizards from a different area. because the data set only maintains its integrity if the new members ofthe sample come from a random sampling. 0 d. They should choose some very heavy lizards. because the data set only maintains its integrity if the mean increases with the sample size. What does the central limit theorem state? O a. The more samples are taken, the more a graph will look like the normal distribution. O b. The more samples are taken, the more centralized the samples will become. O c. The more you run a random experiment, the more centralized its results will become. O d. The more you run a random experiment, the more its results will follow a normal distribution.Which of the following is TRUE according to the central limit theorem? 0 a. The variance of the population can be approximated by the squared variance of the sample means multiplied by the sample size. '3 b. The variance of the population can be approximated by the varianoe of the sample size divided by the sample mean. C} c. The variance of the population can be approximated by the varianoe of the sample means divided by the sample size C} d. The variance of the population can be approximated by the square root of the variance of the sample means multiplied by the sample size. What is the name for the line that goes through the mean of a normal distribution curve? O a. Central line O b. Median O c. Z-score O d. Slope