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 ? (b) (1 point ) How slow do the slowest 45% of West Indian manatees travel '2' (c) (1 point ) You sample 50 West Indian manatees . What is the sampling distribution of their average speed, X? ((1) (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 classified as having gestational diabetes if the glu- cose level is above 140 milligrams per deciliter (mg /dl) 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 p: = 122 mg [CH and a: 12mg /dl. (a) (1 point ) If a single glucose measurement is made , what is the probability that Shelia is diagnosed as having gestational diabetes ? (b) (2 points ) If measurements are made on 4 separate days and the mean result is compared with the criterion 140 mg / d1, what is the probability that Shelia is diagnosed as having gestational diabetes? Question 3 (Each part [1 point ]) The 2010 General Social Survey asked the question : "For how many days during the past 30 days was your mental health , which includes stress , depression, and problems with emotions , not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010 A (a) Interpret this interval in context of the data. (b) What does "95% confident" 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% condence interval? (d) 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 . Assume the standard deviation has remained constant since 2010