1. One type of card stock which may be used for the cover of a booklet is uncoated paper with weight marked as 65 lb. The standard thickness of 65# card stock is 9.5 points (0.0095"). A manufacturer determines that the thickness of 65# card stock produced follows a uniform distribution varying between 9.25 points and 9.75 points. a) Sketch the distribution for this situation. b) Compute the mean and standard deviation of the thickness of the 65# card stock produced. c) Compute the probability that a randomly-selected piece of 65# card stock has a thickness of at least 9.4 points. d) Compute the probability that a randomly-selected piece of 65# card stock has a thickness between 9.45 and 9.75 points.
2. A homeowner has an offer to buy his house for $260,000. A realtor has informed the homeowner that if he is willing to leave the house on the market for another month, he will get between $245,000 and $270,000. Assume that the price that he will get by leaving the house on the market over the next month is uniformly distributed between $245,000 and $270,000. a) If he leaves it on the market for another month, what is the probability he will get less than $260,000? b) If he leaves it on the market for another month, what is the probability he will get more than $260,000? c) What do the probabilities tell you about whether the homeowner should take the $260,000 offer or leave the house on the market for another month?
3. A manufacturer produces metal bars measuring 15 cm using equipment that sometimes malfunctions, causing nicks at various locations on the surface of a bar. Most bars with a nick are defective and must be scrapped. However, if the nick occurs so that the bar can be shortened to 12 cm, the bar can still be sold at the shorter length. Assume that the nicks occur randomly at any location along the 15 cm bar. If a bar is nicked, what is the probability that it can be cut and sold as a 12 cm bar?