question

Consider the probability distribution shown below.

x 0 1 2 P(x) 0.45 0.50 0.05

Compute the expected value of the distribution. (Enter a number.)

Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)

Income range 5-15 15-25 25-35 35-45 45-55 55 or more

Midpoint x 10 20 30 40 50 60

Percent of super shoppers 22% 15% 20% 17% 19% 7%

(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.

Yes. The events are indistinct and the probabilities sum to less than 1.

Yes. The events are distinct and the probabilities sum to 1.

Yes. The events are distinct and the probabilities do not sum to 1.

No. The events are indistinct and the probabilities sum to more than 1.

No. The events are indistinct and the probabilities sum to 1.

Consider a binomial experiment with n = 6 trials where the probability of success on a single trial is p = 0.20. (For each answer, enter a number. Round your answers to three decimal places.)

(a) Find P(r = 0).

(b) Find P(r 1) by using the complement rule.

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that twelve married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)

(a) All of them dislike their mother-in-law.

(b) None of them dislike their mother-in-law.

(c) At least ten of them dislike their mother-in-law.

(d) No more than nine of them dislike their mother-in-law.

Suppose approximately 80% of all marketing personnel are extroverts, whereas about 55% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.)

(a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

What is the probability that 5 or more are extroverts?

What is the probability that all are extroverts?

(b) In a group of 5 computer programmers, what is the probability that none are introverts?

What is the probability that 3 or more are introverts?

What is the probability that all are introverts?

Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following questions.

(a) Would it be unusual to have more than 120 successes out of 200 trials? Explain.

Yes. 120 is more than 2.5 standard deviations above the expected value.

Yes. 120 is more than 2.5 standard deviations below the expected value.

No. 120 is less than 2.5 standard deviations above the expected value.

No. 120 is less than 2.5 standard deviations below the expected value.

(b) Would it be unusual to have fewer than 40 successes out of 200 trials? Explain.

Yes. 40 is more than 2.5 standard deviations above the expected value.

Yes. 40 is more than 2.5 standard deviations below the expected value.

No. 40 is less than 2.5 standard deviations above the expected value.

No. 40 is less than 2.5 standard deviations below the expected value.

(c) Would it be unusual to have from 70 to 90 successes out of 200 trials? Explain.

Yes. 70 to 90 observations is within 2.5 standard deviations of the expected value.

Yes. 70 observations is more than 2.5 standard deviations below the expected value.

No. 70 to 90 observations is within 2.5 standard deviations of the expected value.

No. 90 observations is more than 2.5 standard deviations above the expected value.