Question

5. Suppose X follows a normal distribution with mean u = 200 and standard deviation o = 40. Find each of the following probabilities. (8 points) a. P(160 < x < 232) b. P(X > 160) C. P(X < 100) d. P(230 < x < 284) 6. Sup Suppose we know that SAT scores have a population average u = 1080 and a standard deviation o = 200. A university wants to give merit scholarships to all students with an SAT score above a certain value. They also cannot afford to give scholarships to more than 1.50 percent of applicants (so the probability of being above that cutoff score is .0150). What should the SAT score cutoff to receive a merit scholarship be? (10 points) 7. Suppose we know that a random variable X has a population mean u = 400 with a standard deviation o = 100. What are the following probabilities? (12 points) a. The probability that the sample mean is above 376 when n = 1600. b. The probability that the sample mean is above 376 when n = 400. C. The probability that the sample mean is above 376 when n = 100. d. The probability that the sample mean is above 376 when n = 64. 8. Suppose we know that the population standard deviation for wages (o) is $15. A random sample of n = 900 results in a sample mean wage of $50. (10 points) a. Provide 95% confidence interval estimate of u. Interpret the result. What is the value of the margin of error? b. Provide 90% confidence interval estimate of u. What is the value of the margin of error? c. Provide 99% confidence interval estimate of u. What is the value of the margin of error?

Answer 1

7.900-07- (9.2-72) do Coor-00172) (0017* ld. © T€148.015 £891.-15 (1-57) d.-10 . (i- <z)d Coozat 091.(z)d = (091 x) d (9) =10-6294] +8610-1884-05 (1-72) + (08-072) (08-0727:1-)= (ooz-te: 2 %? "99 ) : ( 262 727 2091 ) d = (7987870912d la 40 0+ 077- 9002= VY

40 Id) P1230 %* (284) =P ( 230-200 CZC 284 - 200) =P(+0.75 CZ2-1) SP (262.1).<P (240-45) : 0.9821-07734 - 10-2087
my dear student as per Chegg rules I have solved the first one question.