Q1. Simulate 100 random normal variables with mean 1.5 and standard deviation 2. Create a histogram which shows the data in the range between -4 and 10. with class intervals of length 0.5 Make sure that your name and current date are also included in the histogram title on this and all the other histograms you generate for this exercise.
Q2. Find out how many of your 100 variables are bigger than 0. and estimate the proba¬bility that a single normal variable with mean 1.5 and standard deviation 2 is above 0. Write this estimate by kind on your histogram. and show on your histogram which area is being used as your estimate. Also, compute and write the theoretical value for this probability using the table of the normal distribution.
Q3. Simulate 100 sample means, each made by taking the average of 20 normal variables with mean 1.5 and standard deviation 2. Make a histogram of these sample means in the range -4 to 10 with class intervals of length 0.5. As in the previous question. estimate the probability that a sample mean is bigger than 0, write this estimate by hand on your histogram, and show which area is being used as the estimate. Also. compute and write the theoretical value for this probability using the table of the normal distribution.
Q4. What do you notice about the two histograms and (therefore) about the two estimates of the probability of getting above 0?