Question 8.56
25. Each year, the study Monitoring the Future: A Continuing Study of American Youth surveys twelfth-grade students on a wide range of topics related to behaviors, attitudes, and values. One of the survey questions asks students to identify their sex. Another question asks students to rate their intelligence compared with others their age. Assume that the sample used in this survey is representative of twelfth-grade students. Here are some of the results from the more than 13,000 students who participated in the survey: 49.8% were male; 50.2% were female; 60.3% of the females rated their intelligence as above average; 68.6% of the males rated their intelligence as above average. Since the number of participants in the survey was large, the survey percentages should be close to the probabilities for the population of twelfth-grade students.
Use probability notation to express each of the percentages above as probabilities.
Find the following probabilities for parts (b) through (e), rounding answers to three decimal places.
- P(female and above average)
- P(male and above average)
- P(above average)
- P(female | above average)
- Suppose a twelfth-grade student is selected at random. Does knowing that the student rated his or her own intelligence as above average increase, decrease, or have no effect on the probability that the student is female? Explain.
25.
(a)
(b)
(c)
(d)
(e)
(f) The probability that a randomly selected student is female is 0.502. On the other hand, if you know that the student rated his/her intelligence as above average, then the probability that the student is female decreases to 0.470.