stats 6.3 HW

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 = 90 and standard deviation 𝜎 = 29. 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 125 (borderline diabetes starts at 125)

(a) .8485 (b) .7549 (c) .6034 (d) .1131

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 44.0 months and a standard deviation of 8.5 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 8% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

(a) 17.36 % (b) 32.02 months

Consider a normal distribution with mean 39 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 39? (Round your answer to two decimal places.)

.50

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 𝜇 = 24; 𝜎 = 3.4

P(x ≥ 30) = .0392

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 𝜇 = 102; 𝜎 = 14

P(x ≥ 90) = .8051

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 𝜇 = 15.8; 𝜎 = 3.5

P(10 ≤ x ≤ 26) = .9497

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 𝜇 = 8; 𝜎 = 2

P(7 ≤ x ≤ 11) = .6247

Suppose 30% of the area under the standard normal curve lies to the right of z. Is z positive or negative?

positive

look at graph Find z such that 3.3% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

z = -1.84

look at graph Find z such that 60% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

z = 0.25

look at graph Find z such that 88.3% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)

z = 1.19