Scores for men on the verbal portion of the SAT-I test arenormally distributed w

Question

Scores for men on the verbal portion of the SAT-I test arenormally distributed with a mean of 509 and a of 112. Randomly selected men are given the Columbia Review Course beforetaking the SAT test. Assume that the course has noeffect. a) If 1 of the men is randomly selected, find the probabilitythat his score is at least 590. b) If 16 of the men are randomly selected, find theprobability that their mean score is at least 590 c) In finding the probability for part (b), why can thecentral limit theorem be used even though the sample size does notexceed 30. d) If the random sample of 16 men does not result in amean score of 590, is there strong evidence to support the claimthat the course is actually effective? why/why not? Scores for men on the verbal portion of the SAT-I test arenormally distributed with a mean of 509 and a of 112. Randomly selected men are given the Columbia Review Course beforetaking the SAT test. Assume that the course has noeffect. a) If 1 of the men is randomly selected, find the probabilitythat his score is at least 590. b) If 16 of the men are randomly selected, find theprobability that their mean score is at least 590 c) In finding the probability for part (b), why can thecentral limit theorem be used even though the sample size does notexceed 30. d) If the random sample of 16 men does not result in amean score of 590, is there strong evidence to support the claimthat the course is actually effective? why/why not?

Explanation / Answer

PART A>>>     Z = (590-509)/ (112/1)   = 0.72 from normal dist tables, Prob ( Z > 0.72) = 0.2358 final answer. PART B>>>     Z = (590 - 509 ) /(112/16) =   2.89 Prob Z > 2.89 = 0.0019 PART C>>> The problem states in black and whitethat the SAT test scores are normally distributed. This isbecause the number of students taking the SAT at a given time arein the tens of thousands, a very very large n. PART D>>> There may or may not be sufficientevidence. You would need more information given tocalculate a confidence interval.   But the simple answerhere is "no". Since the sampling is random, any given samplemay be below 590, above 590, or exactly at 590.   Youwould need to do a confidence interval or do an inferentialstatistical test at some level of significance to determine anylevel of confidence in your conclusion about the value of theReview Course.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.