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# Normal distribution problems

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The number of passengers on the Carnival Sensation during one-week cruises in the Caribbean follows the normal distribution. The mean number of passengers per cruise is 1,820 and the standard deviation is 120.

1. What percent of the cruises will have between 1,820 and 1,970 passengers?
2. What percent of the cruises will have 1,970 passengers or more?
3. What percent of the cruises will have 1,600 or fewer passengers?
4. How many passengers are on the cruises with the fewest 25 percent of passengers?

60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?