It appears I computed the following black circle items wrong. However I am not sure why? Please help! This is my assignment however my tutor marked these wrong and I'm not sure why they are wrong.

Question 1 Using the pen and paper approach how would you compute the probability of a single American adult woman being taller than 180cm? # Pen and paper calculation z=(180-162.6)f6 .4 z # Same result as pen and paper calculation ## [1] 2.71875 # The pnorm gives probability less than 180cm pnorm(180,162.6,6.4) ## [1] 0.9967235 pnorm(2 .72) # Answer is 0.9967359 ## [1] 0.9967359 1-0.9967359 ## [1] 0.0032641 # Multiply probability score by 100 to get percentage 0.0032641*100 # Probability is around 033% #4? [1] 0.32641 a sample of n=10 adult American women are selected what is the mean and standard deviation of the sample mean height? # Use rnorm to generate a sample ofIO women within the range of the mean and standard deviation used from the previous question samplee=rnorm(10,162.6,6.4) 53111pr # Vector with some values ## [1] 162.0015 173.8404 163.0110 161.6301 157.8442 170.4617 158.7328 ## [8] 161.3670 162.8573 158.9207 mean(samplee) ## [1] 163 .0667 sd(samplee) # Each time rnorm is run the output values of the sample are dwerent ## [1] 5.165467 What is the population that the mean height of these 10 women is 180cm or higher? # Pen and paper calculation pnorm(180,162.6882,8.465) # Original values ## [1] 0.9795777 How does the probability from part a compare to the probability from part c? # The probability in part c is higher than part a. This is because women would have a great chance of having a height taller than 180cm in the sample of 1'0, in comparison to the one woman sample. The mean is also a similar value between the two, however the sd is higher for c than a. There is a greater liklihood of heights over 180cm