24. 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 250 days. b) Out of 50 pregnancies, how many would be less than 250 days? c) If 36 women are randomly selected, nd the probability that they have a mean pregnancy between 264 days and 266 days 25. 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. 26. Construct a 95% condence interval for the population mean, u. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2. 27. Consider the condence interval for the population mean (16, 24). Find the margin of error and the sample mean. 28. The P-value for a hypothesis test is P = 0.0237. Do you reject or fail to reject Ho when the level of signicance is 0.05. 29. Given Ho: 11 S 25 and Ha: u > 25, determine whether the hypothesis test is left-tailed, right-tailed, or ham-tailed. 30. Find the P-vaiue for a two-tailed hypothesis test with a test statistic of z = 2.14. Decide whether to reject Ho if the level of signicance is a = 0.05. 3 l . One distributor reports an average of 150 sales per day. You suspect that this average is not accurate, so you randomly select 35 days and determine the number of sales each day. The sample mean is 143 with a standard deviation of 15. At a = 0.01 : a) State the hypotheses, and Identify the claim. b) Find the standardized test statistic z. c) Find the P-value. d) Decide whether to reject the null hypothesis or not. e) Interpret the decision in the context of the original claim. 32. The CEO of the company claims that the mean work day of the company's engineers is less than 8.5 hours. A random sample of 35 of engineers has a mean work day of 8.2 hours with a standard deviation of 0.5 hour. You want to test the CEO's claim at a = 0.01 a) Identify the claim and state the hypothesis b) Find the critical value and identify the rejection region. c) Find the standardized test statistic 2. Sketch a graph. d) Decide whether to reject the null hypothesis. e) Interpret the decision in the context of the original claim. 33. An insurance agent says that the mean cost of insuring a 2008 Honda CRV is more than $1200, A random sample of 7 similar insurance quotes has a mean cost of $1340 and a standard deviation of $55. Is there enough evidence to support the agent's claim at a = 0.10 Assume the population is normally distributed. a) Identify the claim and state the hypothesis b) Find the critical value and identify the rejection region. 0) Find the standardized test statistic 1'. Sketch a graph. d) Decide whether to reject the null hypothesis. e) Interpret the decision in the context of the original claim