1)In a certain year, when she was a high school senior, Idonna scored 670 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 515 and standard deviation 113. Jonathan took the ACT and scored 21 on the mathematics portion. ACT math scores for that year were Normally distributed with mean 20.9 and standard deviation 4.7. Find the standardized scores for both students. (Round your answers to two decimal places.)

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Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?