## Mathematics 340 - Fall 2015

### Homework

Exercises 10.7: 18, 21

Also:

1. A fair coin is tossed 1000 times. Use the Central Limit Theorem to approximate the probability that the number of heads is strictly between 480 and 509.
2. A basketball player makes 80% of her free throws. Use the Central Limit Theorem to approximate the probability that in 80 attempts she makes at least 60.
3. A fair die is rolled 200 times. Use the Central Limit Theorem to approximate the probability that the sum of the rolls is no more than 800.
4. Suppose the lifetime of a certain type of fuse has an exponential distribution with an average lifetime of 3000 hours. Use the Central Limit Theorem to approximate the probability that the sample mean of 100 such fuses will exceed 2950 hours.
5. Suppose the weight of a certain type of widget has a mean of 2 grams and a standard deviation of 0.2 grams. Use the Central Limit Theorem to approximate the probability that 50 of these widgets will weigh more than 102 grams.
6. In American roulette, if a player bets one dollar on a single number, the player wins 35 dollars if the balls lands in that pocket and loses one dollar if the ball lands in any other pocket. Use the Central Limit Theorem to approximate the probability that the total winnings after 1000 such bets is negative.
7. Suppose the number of phone calls arriving at a switchboard has a Poisson distribution with a mean of 20 calls per hour. Use the Central Limit Theorem to approximate the probability that between 17 and 23 calls arrive in an hour. What is the exact probability?

1. 0.5961
2. 0.8962
3. 1
4. 0.5675
5. 0.0793
6. 0.6141
7. Approximation: 0.4246 Exact: 0.4236