3 The mean score on Exam 1 for Ms. Frizzle's class was 78.3%, the median score was 80%. What does this mean about the distribution of the class's scores? (4 points) A) The scores were left-skewed. B) The scores were right-skewed. C) The scores were Normally distributed. D) The scores were bimodal. 4 According to the financial institution Charles Schwab, the mean return for a conservative investment portfolio they offer is 3.27% with a standard deviation of 3.35%. A financial analyst is interested in this portfolio, so he plans on taking a sample of 64 randomly selected portfolios, and then calculating x, the sample mean investment return. Answer the following questions about the sampling distribution of x. i. What is the shape of the sampling distribution of the sample mean? Explain your reasoning with a complete sentence referring to the validity requirements. (2 points) ii. What are the mean and standard error of the sampling distribution of the sample mean? (4 points) x = SEX iii. iv. To compute normal probabilities and values, which GeoGebra application do you need? Circle the correct option to the right. (1 point) x= CAS AGraphics Graphics 2 3D Graphics Spreadsheet Probability Calculator Construction Protocol What GeoGebra inputs would you use to compute the probability that a random sample of 64 portfolios will have an average investment return between 2.5% and 3%? Select the appropriate choice and fill in the empty boxes with the correct input values. Put a "?" where the probability is output. Sketching a graph may help with this. (5 points) Normal (a) (b) Normal (c) Normal EP(X ) = EP PO x ) = x )= V. (Continued from previous page) What GeoGebra inputs would you use to compute the value that separates the 20% of the lowest sample mean investment returns from the rest of the sampling distribution? Select the appropriate choice and fill in the empty boxes with the correct input values. Put a ? where the mean investment return is output. Sketching a graph may help with this. (5 points) vi. Normal (a) EP(X ) = (b) Normal EEP( Normal )= HEP x ) = The GeoGebra output given below was computed using the mean and standard deviation of the sampling distribution for sample means when n = 64. ] [] ] [ P(X 2.5 ) = 0.033 Interpret this output by completing the following sentence: (2 points) For 100 samples of size 64, we would expect about return less than 2.5%. samples to have a sample mean investment