PROBABILITY (with solutions)

1. The nicotine content of a certain brand of king size cigarette has a normal distribution with a mean content of 1.30 mg and a standard deviation of 0.20 mg. Find the probability that the nicotine of a randomly picked cigarette of this brand will be {a} between 1.45 mg and 1.65 mg and (b) more than 2.15 mg. 2. Janelle plays a game in which she chooses a card at random from a standard deck of 52 cards. lfthe card selected is a face card, she wins $2; if it is an ace, she wins $5; it it is an even numbered card, she wins $1; but if it is an odd numbered card, she loses $3. Find her expected gain for this game. 3. A certain type of rope has an average breaking strength of 1,200 pounds. If the standard deviation is 100 pounds, find the probability that a randomly selected piece of rope will break under a strain of less than 1,000 pounds