The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 54 ounces and a standard deviation of 7 ounces. Use the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 47 and 75 ounces? % c) What percentage of the widget weights lie below 68 ? %

Internet Service Providers The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $50 and the standard deviation is $20. The distribution is not Normal: many households pay a low rate as part of a bundle with phone or television service, but some pay much more for Internet only or for faster connections. A sample survey asks an SRS of 50 households with Internet access how much they pay. Let x be the mean amount paid. 1. Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds $55. 2. What are the mean and standard deviation of the sampling distribution of x ? 3. What is the shape of the sampling distribution of x ? Justify your answer. 4. Find the probability that the average fee paid by the sample of households exceeds $55.

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Use the grouped data formulas to find the indicated mean or standard deviation. For the following data set, approximate the sample standard deviation. Height (in inches) Frequency 50-52 53-55 56-58 12 59-61 13 62-64 11 E