Consider a binomial experiment with n = 20 trials and p = 0.40. (a) Find the expected value and the standard deviation of the distribution. (Please answer standard deviation in 2 decimal places after decimal point.)

Expected Number ANSWER:

Standard Deviation ANSWER:

(b) Would it be unusual to obtain fewer than 3 successes? ANSWER:

2. In the book A Guide to the Development and Use of the Myers-Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with six different professors. (a)What is the probability that all six are extroverts? (Please answer in 3 decimal places after the decimal point.)

ANSWER

(b)What is the probability that none of your professors is an extrovert? (Please answer in 3 decimal places after the decimal point.)

ANSWER:

(c) What is the probability that at least two of your professors are extroverts? (Please answer in 3 decimal places after the decimal point.)

(d) In a group of six professors selected at random, what is the expected number of extroverts? What is the standard deviation? (Please answer expected number in 1 decimal place after decimal point. Please answer standard deviation in 3 decimal places after decimal point.)

Expected Number ANSWER:

Standard Deviation ANSWER:

3. About 25% of those called for jury duty will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty (Source: Bernice Kanner, Are You Normal?, St. Martin's Press). (a) If 12 people are called for jury duty, what is the probability that all 12 will be available to serve on the jury? (Please answer in 3 decimal places after the decimal point.)

ANSWER:

(b) If 12 people are called for jury duty, what is the probability that 6 or more will not be available to serve on the jury? (Please answer in 3 decimal places after the decimal point.)

ANSWER:

(c) Find the expected number of those available to serve on the jury.

ANSWER

(d) What is the standard deviation? (Please answer in 1 decimal place after decimal point.)