Question 1 West Indian manatees travel at a speed that is approximately normally distributed with a mean of 3.8 miles per hour and a standard deviation of 1.34 miles per hour . (a) (2 points) What proportion of West Indian manatees travel at speeds between 3 and 4.7 miles per hour? (1)) (2 points) How slow do the slowest 45% of West Indian manatees travel? (c) (2 points) You sample 50 West Indian manatees. What is the sampling distribution of their average speed, X? (d) [2 points ) What is the probability that the mean speed of your sample is between 3 and 4.7 miles per hour? Question 2 Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy ). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is cLassied as having gestational diabetes if the glu cose level is above 140 milligrams per deciliter (mg J.Ildl) one hour after having a sugary drink . Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with it = 122 mg {dl and a: 12mg fdl. (a) ( 2 points ) If a single glucose measurement is made , what is the probability that Shelia is diagnosed as having gestational diabetes ? (b) (3 points ) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg ,1 (11, what is the probability that Shelia is diagnosed as having gestational diabetes? Question 3 Question 4.12 in the text book ( each part [2 points ], total [8 points ]) The 2010 General Social Survey asked the question: "For how many days during the past 30 days was your mental health1 which includes stress, depression, and problems with emotions, not good ?' Based on realmnses from 1,151 US residents , the survey reported a 95% condence interval of 3.40 to 4.24 days in 2010. (a) Interpret this interval in context of the data. (b) What does "95% condent ' mean ? Explain in the context of the application (c) Suppose the researchers think a 99% condence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval? ((1) If a new survey were to be done with 500 Americans , would the standard error of the esti mate be larger , smaller , or about the same _ Asslnne the standard deviation has remained constant since 2010. Question 4 Question 4.14 in the text book . ( each part [1 point ], total ['1' points ])