Exercises. 1. For a binomial probability distribution, n =80 and p =0.50

1. For a binomial probability distribution, n =80 and p =0.50. Let x be the number of successes in 80 trials.

a) Find the mean and standard deviation of the binomial distribution.

b) Find using the normal approximation.

c) Find using the normal approximation

2. For a binomial probability distribution, n =120 and p =0.6. Let x be the number of successes in 120 trials.

a) Find the mean and standard deviation of the binomial distribution.

b) Find using the normal approximation.

c) Find using the normal approximation

3. Find the following binomial probabilities using the normal approximation

a) n =70; p =0.30;

b) n =200; p =0.70;

c) n =40; p =0.25;

d) n =50; p =0.10;

4. According to the statistics, 19% of cars in the city were at least 12 years old in 2004. Assume that this result holds true for the current population of all cars in the city. Random sample of 500 cars are selected at random. Find the probability that

a) exactly 92 cars are at least 12 years old.

b)100 or more cars are at least 12 years old.

c) 90 to 98 cars are at least 12 years old?

5. Accordingto a survey, 30% of credit card holders pay off their balances in full each month. Assume that this result holds true for the current population of credit card holders.

a) Find the probability that in a random sample of 400 credit card holders, exactly 125 pay off their balances in full each month.

b) Find the probability that in a random sample of 400 credit card holders, at least 110 pay off their balances in full each month.

c) What is the probability that in a random sample of 400 credit card holders, 115 to 130 pay off their balances in full each month?

6. A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 70% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that 70% of all people like this hamburger. On a certain day, 40 customers bought this hamburger.

a) Find the probability that exactly 32 of the 40 customers will like this hamburger.

b) What is the probability that 25 or less of the 40 customers will like this hamburger?

c) What is the probability that 31 to 34 of the 40 customers will like this hamburger?

7. According to a survey, 20.8% of the lawyers and judges are women.

a) Find the probability that in a random sample of 200 lawyers and judges, exactly 35 are women.

b) Find the probability that in a random sample of 200 lawyers and judges, at most 45 are women.

c) What is the probability that in a random sample of 200 lawyers and judges, 43 to 50 are women?

8. Of the customers visiting the stereo section of a large electronic store, only 25% make a purchase. If 45 customers visit the stereo section tomorrow, find the probability that more than 10 will make a purchase.

9. The unemployment rate in a city is 7.9%. A sample of 100 persons is selected from the labor force. Approximate the probability that

a) less than 11 unemployed persons are in the sample

b) more than 9 unemployed persons are in the sample.

c) between 8 and 12 unemployed persons are in the sample.

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