An investment company knows tht he ratesFreturn on its portfolios have a mean OT745 percent, with a standard deviation of 3.82 percent. The company selects a sample of 144 . portfolios to analyze. Assume the company has tens of thousands of portfolios. (Careful- percent" is just a unit here!) 4. What is the probability that the mean of the sample is larger than 8 percent? 5. What is the probability that the mean of the sample is smaller than 7.6 percent? 6. What is the probability that the mean of the sample is between 7.1 and 8.1 percent? 19. In the United States, the population mean height for 4-year-old boys is 39 inches. Suppose a random sample of 32 non-U.S. 4-year-old boys showed a sample mean of 38.2 inches with a standard deviation of 3.1 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. (a) State the null and alternative hypotheses (b) Compute the test statistic m-332 ne3S-3 32 20. The National Highway Traffic Safety Administration (NHTSA) stated that the percentage of people who used their seatbelts in the year 2002 was 71%. The NHTSA also reported that a random sample of 3005 people showed that 2104 reported using their seatbelts in 2012. Conduct a hypotheses test at a significance level of 10% to see whether the percentage of people who used their seatbelts in 2012 changed from the 71% reported in the year 2002