Question 1076108: 1.)A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 87 and standard deviation σ = 28. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
a.) x is more than 60
b.) x is less than 110
c.) x is between 60 and 110
d.) x is greater than 140 ( borderline diabetes starts at 140)
2.)Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 35 and standard deviation σ = 11. Find the following probabilities. (Round your answers to four decimal places.)
(a) x is less than 60
(b) x is greater than 16
(c) x is between 16 and 60
(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)
3.)Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.7 millimeters (mm) and a standard deviation of 0.9 mm. 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
4.)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 of 8.9 minutes and a standard deviation of 1.6 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)
(a) the response time is between 5 and 10 minutes
(b) the response time is less than 5 minutes
(c) the response time is more than 10 minutes
5.)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 of 45.2 months and a standard deviation of 8.9 months.
(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 than 7% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
months
6.)Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 35 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 7 months, and the distribution of lifetimes is normal.
(a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)
(b) If Accrotime does not want to make refunds on more than 10% of the watches it makes, how long should the guarantee period be (to the nearest month)?
months
Answer by ikleyn(52803)   (Show Source):
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