Read all directions carefully. Unless otherwise indicated, round your only nal answers (not the middle steps) to two decimal places. There is hint given for problems you might want to use. Problem # 5. The number of calories in a 1.5-ounce chocolate bar is 225. Suppose that the distribution of calories is normally distributed with the standard deviation 0' = 10. a) What is the probability that a randomly selected chocolate bar will have between 200 and 220 calories? Show all your steps. Hint: use the formula for z-score and then use the ztable. b) What is the probability that a randomly selected chocolate bar will have less than 190 calories? Show all your steps. Hint: use the formula for z-score and then use the ztable. Problem # 6. Dr. Mendoza developed a test to measure boredom tolerance. The test results for the group of 20,000 adults are shown in the following table. Determine if the table satisfies a probability distribution. If yes, find the mean, variance, and standard deviation? Show all your steps. X P(X) X *P(X) (X- M ) 2 (X - H) 2 *P(X) 0 0.07 0.13 2 0.18 W 0.30 4 0.22 5 0.10