21. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a) Find the probability that the length of pregnancy is less than 266 days. b) Out of 200 pregnancies, how many would be less than 266 days? c) If 36 women are randomly selected, nd the probability that they have a mean pregnancy between 264 days and 266 days. 22. A random sample of 40 students has a test score with mean 31.5. Assume the population standard deviation is 10.2. Construct the 90% condence interval for the population mean. 23. Construct a 95% condence interval for the population mean, u. Asslnne the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 31.5 with a standard deviation of 10.2. 24. The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 95% certain that we are within 4 points of the true mean. Find the sample size. 25. Consider the condence interval for the population mean (16, 24). Find the sample mean it and the margin of error E. 26. State the hypothesis, and identify the claim. \"A company advertises that the mean life of its furnaces is at least 15 years.\" 2?.The statement p = 3.8 represents a claim. Write its complement and state which is Ho and which is H3. 28. Given Hg: [.1 5 25 and H.: p 3:- 25, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. 29. Find the Pvalne for a two-tailed hypothesis test with a standardized test statistic of: = - 2.14. 3!}. The P-value for a hypothesis test is P = 0.0232. Do you reject or fail to reject 1-10 at n = {1.05. 31. Find the critical value to for a Left-tailed test with n = 0.10 and n = 22