can this be done in standard deviation

trial of Microsoft 365 or sign in to activate an existing subscription. Statistics Prof. Miller Measures of Central Tendency and Dispersion 1. A manufacturer of pencils is choosing between two pencil making machines. Machine A produces pencils which have a mean length of 6 inches and a standard deviation of 0.18 inch while machine B produces pencils which have a mean length of 6 inches and a standard deviation of 0.08 inch. Which machine should the manufacturer choose and why? 2. A marketing researcher asked 80 adults how many times they went grocery shopping in the last month. Find the standard deviation for the survey responses summarized in the table below where x is the number of + grocery trips and f is the frequency of that response: X: 3 6 8 10 12 13 20 number of store visits F: 10 18 12 10 22 2 frequency 3. The following data are the price of gas at 16 gas stations (in $/gallon): 3.06 3.09 3.14 3.19 3.20 3.25 3.25 3.26 3.26 3.28 3.29 3.29 3.38 3.41 3.52 3.59 (a) Find the mean and standard deviation for the given data. (b) What proportion of the data lies within: * one standard deviation of the mean * two standard deviations of the mean three standard deviations of the mean