Statistics

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The wldget weights have a mean of 62 ounces and a standard deviation oi 7 ounces. Use the Standard Deviation Rule. also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a] 99.7% of the widget weights lie between I: and bl What percentage of the widget weights lie between 55 and 83 ounces? :] 95 c} What percentage of the widget weights lie below '16 ? [: iii A company has a policy of retiring company cars; this policy looks at number of miles driven. purpose of trips. style of car and other features. The distribution of the number of months In service for the eet of cars Is bell-shaped and has a mean of 61 months and a standard deviation of 5 months. Using the empirical rule (as presented in the book}, what is die approximate percentage of cars that remain in service between 71 and 76 months? Do not enter the percent symbol. Fill In the blanks. In a normal distribution, I: percent of the data are above the mean. and :] percent of the data are below the mean. Similariy. [: percent of all data points are within 1 standard deviation of the mean. :] percent of all data points are within 2 standard deviations of the mean, and :] percent are within 3 standard deviations of the mean. In a normal distribution. a data value located 0.5 standard deviations below the mean has Standard Score: 2 = C] In a normal distribution. a data value located 2.1 standard deviations above the mean has Standard Score: 2 = C] In a normal distribution. the mean has Standard Score: 2 = :l 1. Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2.39 days {note that times are measured continuously, not just in number of days). A random sample of 124 shipments are selected and their shipping times are observed. Approximate the probability that the average shipping time Is less than 2.01 days. 2. The useful life of a bicycle bought at Basement-mart fits a log normal distribution with a mean of 23 months and a standard deviation of 12.25 months. Suppose that 53 bicycles are randomly chosen, and let X_= the average useful life of a bicycle bought at Basement-mart, from a sample of 53 bicycles (in months)