The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean=$635and standard deviation=$38.(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.) (b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only0.14? (Round your answer to the nearest dollar.) $

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Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of43.8months and a standard deviation of7.7months.(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.) % (b) If Quick Start does not want to make refunds for more than6%of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months

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Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of6.8minutes and a standard deviation of1.9minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)(a) the response time is between3and8minutes (b) the response time is less than3minutes (c) the response time is more than8minutes

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Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of4.8millimeters (mm) and a standard deviation of1.0mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)(a) the thickness is less than 3.0 mm (b) the thickness is more than 7.0 mm (c) the thickness is between 3.0 mm and 7.0 mm

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Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Letxbe a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles,xis approximately normally distributed with mean=41and standard deviation=14.Find the following probabilities. (Round your answers to four decimal places.)(a)xis less than 60 (b)xis greater than 16 (c)xis between 16 and 60 (d)xis more than 60 (This may indicate an infection, anemia, or another type of illness.)

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A person's blood glucose level and diabetes are closely related. Letxbe a random variable measured in milligrams of glucose per deciliter(1/10 of a liter)of blood. Suppose that after a12-hourfast, the random variablexwill have a distribution that is approximately normal with mean=90and standard deviation=26.Note:After 50 years of age, both the mean and standard deviation tend to increase. For an adult(under 50)after a12-hourfast, find the following probabilities. (Round your answers to four decimal places.)(a)xis more than 60 (b)xis less than 110 (c)xis between 60 and 110 (d)xis greater than 125 (borderline diabetes starts at 125)

A person's blood glucose level and diabetes are closely related. Letxbe a random variable measured in milligrams of glucose per deciliter(1/10 of a liter)of blood. Suppose that after a12-hourfast, the random variablexwill have a distribution that is approximately normal with mean=90and standard deviation=26.Note:After 50 years of age, both the mean and standard deviation tend to increase. For an adult(under 50)after a12-hourfast, find the following probabilities. (Round your answers to four decimal places.)(a)xis more than 60 (b)xis less than 110 (c)xis between 60 and 110 (d)xis greater th

an 125 (borderline diabetes starts at 125)