4. Aviation Work and Space Technology, February 2005, reported that 2004 was a recovery year for the general aviation industry. Worldwide, planes with piston engines accounted for 70% of all sales. Suppose that 100 planes that were sold in 2004 were randomly selected. (a) (5 points) Show that this problem satisfies the requirements for using the normal approx- imation model. Use Statcrunch or the standard normal table to answer the following ques- tion (in either case you MUST include a picture for full credit). Include all probability notation.: (b) (5 points) What is the probability that 75 or more of them had piston engines? hp5. The administrator for a hospital for head injury patients reports that, for patients who have received treatment at the hospital, the mean score on a test to measure vocational readiness is 95 points and the standard deviation is 5 points. A therapist randomly samples 50 recent patient records and notes the score on the test for each patient. Use Statcrunch or the standard normal table to answer the following questions (in either case you MUST include a picture for full credit). Include all probability notation. (a) (5 points) What is the probability that the mean score of the sample is between 91 and 99 points?(b) (5 points) What score must you be under to be in the bottom 10% of scores