Determine if the following statement is true or false. The normal curve is symmetric about its mean, u. Choose the best answer below. A. The statement is true. The normal curve is a symmetric distribution with one peak, which means the mean, median, and mode are all equal. Therefore, the normal curve is symmetric about the mean, J. O B. The statement is false. The normal curve is not symmetric about its mean, because the mean is the balancing point of the graph of the distribution. The median is the point where 50% of the area under the distribution is to the left and 50% to the right. Therefore, the normal curve could only be symmetric about its median, not about its mean. O C. The statement is true. The m balancing point for the graph of a distribution, and therefore, all distributions are symmetric about the mean. D. The statement is false. The mean is the balancing point for the graph of a distribution, and therefore, it is impossible for any distribution to be symmetric about the mean. 2. Complete the statement below The points at x= and x = are the inflection points on the normal curve. What are the two points? O A. The points are x = H - 30 and x = | + 30. O B. The points are x = HI - 20 and x = | + 26. O C. The points are x = u - o and x = | + 6. 3. Determine whether the following graph can represent a normal density function. Could the graph represent a normal density function? Yes No 4. Determine whether the following graph can represent a normal density function. Could the graph represent a normal density function? Yes No 5. A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal 0.4- distribution could be used as a model for the variable. 2000 3000 4000 Choose the correct answer below. A. The histogram is not bell-shaped, so a normal distribution could be used as a model for the variable. O B. The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable. O C. The histogram is bell-shaped, so a norm istribution could be used as a model for the variable. D. The histogram is bell-sha variable. istribution could not be used as a model for the 6. T e relative frequency histogram represents the length of phone calls on George's cell phone during the month of September. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable. Relative Frequency Length (minutes) Can a normal distribution be used as a model for the variable? O A. Yes, beca ormal curve. O B. No, because the histogram has the shape of a normal curve. O C. Yes, because the histogram does not have the shape of a normal curve. D. Yes, because the histogram is not symmetric about its mean. O E. No, beca histogram does e the shape of a normal curve. One graph in the figure represents a epresents a normal distribution with mean u = 15 and standard deviation o=3. The other graph represents a normal distribution with mean u = 7 and standard deviation < =3. Determine which graph is which and explain how you know. Choose the correct answer below. A. Graph A has a mean of u = 15 and graph B has a mean e a larger mean shifts the graph to the right. B. Graph A has a mean of u = 7 and graph B has a mea mean shifts the graph to the left. C. Graph A has a mean of u = 15 and graph B has mean shifts the graph to the left. D. Graph A has a mean of u = 7 and graph B has a mean of u = 15 because a larger mean shifts the graph to the right. 8. The graph of a normal curve is given on the right. Use the graph to identify the values of u and G. 16- 15-14-13-12-41-10 Suppose the monthly charges for cell phone plans are normally distributed with mean u = $60 and standard deviation G= $18. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of plans that charge less than $42. (c) Suppose the area under the normal curve to the left of X = $42 is 0.1587. Provide an interpretation of this result. (a) Choose the correct graph below. OA OB. O C. OD. (b) Choose the correct graph below. OA OB O c. OD. 4 42 60 (c) Select the correct choice below and fill in the answ e your choice. (Type a whole number.) A. The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $ per month. O B. The probability is 0.1587 that a randomly selected cell phone plan in this population is more than $ per month