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November 20th, 2008, 07:39 PM
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1. A telemarketer found that there was a 2% chance of a sale from his phone solicitations. If 1000 telephone calls were made, use the normal approximation to the binomial distribution to find the probabilities that
a) at most 20 sales were made;
b) more than 30 sales were made;
c) exactly 25 sales were made
2. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. If 100 women are randomly selected,
a) find the mean and standard of error of the mean of the sampling distribution of sample means;
b) What happens to the mean and standard deviation of the distribution of sample means when the sample size is increased to 225?
c) Find the probability that the mean length of pregnancy, X (x bar)for a random sample of 100 women is more than 275 days
3. Commonly used practice of airline companies is to sell more tickets than actual seats to a particular flight because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no shows at flight time is 3%. For a particular flight with 195 seats, a total of 200 tickets were sold. What is the probability that the airline overbooked this flight?  |
November 22nd, 2008, 01:22 AM
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Quote:
Originally Posted by hidaja16  1. A telemarketer found that there was a 2% chance of a sale from his phone solicitations. If 1000 telephone calls were made, use the normal approximation to the binomial distribution to find the probabilities that
a) at most 20 sales were made;
b) more than 30 sales were made;
c) exactly 25 sales were made
Mr F says: The first thing you need to do is state the normal approximation to the binomial distribution. After you've done that, please state where you get stuck.
2. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. If 100 women are randomly selected,
a) find the mean and standard of error of the mean of the sampling distribution of sample means;
Mr F says: Mean = 268. Standard error = sigma = 15/sqrt{100} = 1.5.
b) What happens to the mean and standard deviation of the distribution of sample means when the sample size is increased to 225?
Mr F says: Consider the formulae I used to answer a).
c) Find the probability that the mean length of pregnancy, X (x bar)for a random sample of 100 women is more than 275 days
Mr F says: Since X bar follows a normal distribution with mean and standard deviation as stated in a) you should be able to answer this after considering the replies I've given to your other posts.
3. Commonly used practice of airline companies is to sell more tickets than actual seats to a particular flight because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no shows at flight time is 3%. For a particular flight with 195 seats, a total of 200 tickets were sold. What is the probability that the airline overbooked this flight? | 3. Let X be the random variable number of no shows at a flight.
X ~ Binomial(n = 200, p = 0.03).
Calculate Pr(X < 5).
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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