Highpressure washers have become popular for cleaning siding, decks, and windows. This equipment is available in various engine types and horsepower. Suppose the power rating (in horsepower, hp) for a residential pressure washer is normally distributed with mean 20 hp and standard deviation s.
a. The probability that a randomly selected power rating is within 2.5 hp of the mean is 0.7229. Find the value of s.
b. A leading consumer magazine advised its readers to purchase pressure washers with a power rating of 15 hp or more. What proportion of pressure washers have this rating?
c. If the power rating is more than 26.5 hp, the pressure washer will crack, or even break, certain windows. What is the probability that a pressure washer could break a window?
Hydroelectric projects are carefully monitored, and their energy capability is predicted for several years into the future. Suppose the Klamath Hydro Project, located on the upper Klamath River in south-central Oregon, generates electricity according to a normal distribution. The Pacific Northwest Utilities Conference Committee claims the mean electricity generated per year is 35 megawatts (MW).
a. The probability that the Klamath Hydro Project generates less than 34 MW during any randomly selected year is 0.3540. Find the standard deviation.
b. Suppose the years are independent, and the hydro project will record a profit in a given year if it is able to generate at least 37.8 MW that year. What is the probability that the project will record a profit for four consecutive years?
c. Suppose the electricity generated during a certain year is 33.5 MW. Is there any evidence to suggest that the claim by the Pacific Northwest Utilities Conference Committee is false? Justify your answer.
Diningroom chairs come in many different woods, styles, and shapes. The height of the seat of a randomly selected oak dining-room chair is approximately normal with mean 85 centimeters (cm) and standard deviation 1.88 cm.
a. Find a value h such that 99% of all dining-room chairs have height less than h.
b. Consumer testing indicates that any chair seat higher than 90 cm is uncomfortable to use when eating. What is the probability that a randomly selected dining-room chair is uncomfortable?
c. Find the first and third quartiles of the dining-room chair height distribution.
d. There is some evidence to suggest that, after five years of use, the mean height of these chairs has decreased, due to wear, erosion, and humidity. Suppose that after five years, the probability the height is more than 86 cm is 0.0718. Find the mean height after five years.