numerical analysis

1) (a) Calculate the expected value and standard deviation of this random variable X by using the probability distribution shown. (b) Describe the shape of this distribution. x P(x) 60 0.40 70 0.30 80 0.20 90 0.10 Chap 7 Remember, all z values should be rounded properly to 2 decimal places. All probabilities should maintain at least FOUR decimal places. For instance, if you final probability answer is .3512, do NOT round it to .35, or 35%. Keep it at .3512, or 35.12% 2) 16 pts Using your normal distribution tables, find the normal probabilities associated with the following: Be sure to show work for partial credit a. P(-1.22 < Z < 2.15) b. P(2.00 < Z < 3.20) c. P(−3.00 < Z < 3.00) d. P(Z < 0.50) . 3) (15 pts) The weight of a Nestle bar has a mean of 3.2 grams and a standard deviation of .15 grams. The weights are normally distributed. (a) Within what weight range will the middle 90 percent of all bars fall? (b) What is the probability that a randomly chosen bar will weigh less than 3.52 grams? c) What is the probability that a randomly chosen bar will weigh between 3.15 and 3.45 grams? 4) 15 pts Twenty five year old mortgage applicants at a local credit union have credit scores that are normally distributed with a mean of 500 and a standard deviation of 100. (a) Find the credit score that defines the upper 5 percent. (b) Sixty-five percent of the customers will have a credit score higher than what value? (c) Within what range would the middle 80 percent of credit scores lie? 5) 6 pts Which of the following is/are a continuous random variable? a. Weight of dogs in the pound b. liters of milk in a bottle. c. number of pens on a desk.. 6) 15 pts The stamping machines in a production facility have a mean weight of 579 lbs with a standard deviation of 14 lbs. (a) What is the probability that a randomly chosen machine will weigh less than 579 lbs? (b) More than 590 lbs? (c) Less than 600 lbs?