Question 4 An automatic ball-throwing machine is a device that tosses objects such as baseballs, softballs, and footballs at specified speeds. The machine’s manufacturer, Beanball, has constructed the device so that there was little variance in the velocities of the projectiles. For example, if a machine were to be set at a mean output of 90 miles per hour (mph), its standard deviation would remain 3 mph. Assuming that the variation of the speeds is normally distributed, please answer the following questions about a machine set to throw at 90 mph.:
a. What is the probability of a ball being thrown at more than 95 mph?
b. What is the probability of a ball being thrown between 86 and 92 mph?
c. If Beanball wanted to reset the machine so that only 2 in 1000 balls would have velocities of less than 85 mph, what should be the mean output of the machine be set to?
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