Computer Science Data Science problems
I will give thumb up, thank you!
You bring many donuts (or doughnuts, if you will) to work to share with your coworkers at the Boulder Nuclear Power Planet. But due to the high levels of radiation there, they must be inspected for safety. In particular, if the mean level of radiation in a sample fronm your batch of donuts is above 200 mSv (millisievert), then they are deemed unsafe and you must throw the whole batch away. You know that historically donuts at the power plant have, on average, 190 mSv of radiation, with a standard deviation of 40 mSv. To test the donut radiation levels, you take the donut receipt and pick every fifth donut off it, and sample the radiation levels of those donuts. You end up sampling the radiation levels of 36 donuts out of the batch Part A. What is the probability that a donut batch is deemed unsafe? You should at the very least set up and justify your calculation by hand (in Markdown/Mathjax), before executing any calculations in Python. Part B. You really do not want to throw away donuts that frequently, so you propose to store the donuts in a lead-lined donut box. But lead also is not very good for your health, so you are motivated to use the least amount of lead possible. What is the maximum mearn of the donut radiation distribution such that the probability that we will throw donuts out due to safety concerns is at most 0.001? Assume that the variance and sample size remain the same as above. Calculate this by hand, using Python only to prform arithmetic operations and compute critical values of a standard normal random variable Part C. Your supervisor at the plant decides that serving up donuts in a lead-lined box is a bad idea. Fair enough But she is still imposing the requirement that the probability of a batch of donuts being rejected must be less than 0.001. Suppose the mean and standard deviation are at their original values of = 190 mSv and = 40 mSv. what is the minimum sample size to satisfy this requirement? Calculate this by hand, using Python only to prform arithmetic operations and compute critical values of a standard normal random variable Part D. Can you think of any potential issues with using a normal distribution to model the radiation content of our donuts? You bring many donuts (or doughnuts, if you will) to work to share with your coworkers at the Boulder Nuclear Power Planet. But due to the high levels of radiation there, they must be inspected for safety. In particular, if the mean level of radiation in a sample fronm your batch of donuts is above 200 mSv (millisievert), then they are deemed unsafe and you must throw the whole batch away. You know that historically donuts at the power plant have, on average, 190 mSv of radiation, with a standard deviation of 40 mSv. To test the donut radiation levels, you take the donut receipt and pick every fifth donut off it, and sample the radiation levels of those donuts. You end up sampling the radiation levels of 36 donuts out of the batch Part A. What is the probability that a donut batch is deemed unsafe? You should at the very least set up and justify your calculation by hand (in Markdown/Mathjax), before executing any calculations in Python. Part B. You really do not want to throw away donuts that frequently, so you propose to store the donuts in a lead-lined donut box. But lead also is not very good for your health, so you are motivated to use the least amount of lead possible. What is the maximum mearn of the donut radiation distribution such that the probability that we will throw donuts out due to safety concerns is at most 0.001? Assume that the variance and sample size remain the same as above. Calculate this by hand, using Python only to prform arithmetic operations and compute critical values of a standard normal random variable Part C. Your supervisor at the plant decides that serving up donuts in a lead-lined box is a bad idea. Fair enough But she is still imposing the requirement that the probability of a batch of donuts being rejected must be less than 0.001. Suppose the mean and standard deviation are at their original values of = 190 mSv and = 40 mSv. what is the minimum sample size to satisfy this requirement? Calculate this by hand, using Python only to prform arithmetic operations and compute critical values of a standard normal random variable Part D. Can you think of any potential issues with using a normal distribution to model the radiation content of our donuts
