QUESTION 1 a. Using the pen-and-paper approach, show how you would compute the probability of a single American adult woman being taller than 180 cm. Assume heights are normally distributed. Now use R to compute your final answer. Hint: the data for this question are in the NASA table above. b. Using the pen-and-paper approach, show how you would compute the probability of a single American adult woman being between 160 and 180 cm in height? Use R to verify your final answer. c. If a sample of n = 10 adult American women are selected what is the mean and standard error of the mean for height?Exercise: NASA pen-and-paper NASA excludes from the astronaut program anyone less than 148.6 cm or more than 193.0 cm in height. Assuming the heights are normally distributed, compute the proportion of men who are excluded from astronaut training. Mean Standard Deviation Males 175.6 7.1 Females 162.6 6.4 Step 1: To easily visualise these problems you should first draw a sketch. Since 148.6 and 193 falls in the tails of the distribution, you can hardly see any shading under the curve. Density 0.00 0.01 0.02 0.03 0.04 0.05 150 160 170 180 190 200 X