Answer the following: a) The temperature recorded by a certain thermometer when placed in boiling water (true temperature 100* C) is normally distributed with mean ( =99.8'C and standard deviation o =0.1'C. What is the 2 probability that the thermometer reading is within +0.05'c of the true temperature? b) If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value. c) A machine used to extract juice from oranges obtains an amount from each orange that is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounces. Ninety percent of the oranges will contain an amount that is between what two values (symmetrically distributed around the mean)