4. A basket contains 19 eggs, 4 of which are cracked. If we randomly select 11 of the eggs for hard boiling, what is the probability of the following events?.

(b) None of the eggs selected are cracked.

(c) Two of the crack eggs are selected.

5. Determine if the following random variables are discrete or continuous.

(a) Time required to download a file from the internet.

(b) Number of hits on a website.

(c) Amount of rain during October.

(d) Number of days it rains in October.

I understand this one, but what is a really good way to tell the difference?

6. Let the random variable x represent the number of girls in a family with 3 children. The probability of a child being a girl is 0.44. Construct a table describing the probability distribution, the find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls?

(a)

x P(x)

0

1

2

3

(b) Mean =

(c) Standard Deviation =

(d) Is it unusual for a family of three children to have only girls?

7. Do the following represent a binomial experiment? Explain.

(a) Five cards are selected from a standard 52-card deck without replacement. The number of diamonds selected is recorded.

(b) An experimental drug is administered to 110 randomly selected individuals, with the number of individuals responding favorably recorded.

8. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use a binomial probabilities table to find the probability of x successes given the probability p of a success on a given trial.

(a) n=7, x=2, p=0.50

(b) n=6, x=3, p=0.25

9. The binomial distribution below is from a clinical test of a drug, 16.3% of the subjects treated with 10mg of the drug experienced headaches. In each case, assume that 5 subjects are randomly selected and treated with 10 mg of the drug.

n = 5, p=0.163

x P(x)

0 0.4108

1 0.4000

2 0.1558

3 0.0303

4 0.0030

5 0.0001

(a) Find the probability that more than one subject experience headaches.

(b) Find the probability 3 or more subjects experience headaches.

(c) Find the mean

(d) Find the standard deviation

(e) Find the maximum usual value

(f) Find the minimum usual value

(g) Is it unusual for 3or more subjects to experience headaches?

10. A candy company claims that 24% of its plain candies are orange and a sample of 200 such candies is randomly selected.

(a) Find the mean.

(b) Find the standard deviation

(c) A random sample of 200 candies contains 34 orange candies. Is the result usual? What can you say about the claim of 24%?

Excel Exercise:

Use Excel to check your answers to the following. Please place the Excel spreadsheet in the drop box demonstrating that you can do these things in Excel. Help is provided in a spreadsheet.

#3 Please calculate (a), (b), and (c) using Excel

#9 Please use Excel to generate the binomial probability distribution. Then check your answers to (a) and (b) using Excel.