Question

1. 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, xis approximately normally distributed with mean μ = 42 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.)

2. 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 46.2 months and a standard deviation of 6.5 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 14% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
___________months

3. 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 = 39; σ = 15

P(50 ≤ x ≤ 70) =

Answer 1