Full marks: 30 marks Show your calculation steps clearly. Correct you answer to 4 decimal places and report the measurem

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Full Marks 30 Marks Show Your Calculation Steps Clearly Correct You Answer To 4 Decimal Places And Report The Measurem 1 (115.86 KiB) Viewed 33 times

Full marks: 30 marks Show your calculation steps clearly. Correct you answer to 4 decimal places and report the measurement unit when applicable. Question 1 (10) marks) A salad shop is selling fruit cups. Each fruit cup consists of two types of fruit, strawberries and blue berries. The weight of strawberries in a fruit cup is normally distributed with mean 160 grams and standard deviation 10 grams. The weight of blue berries in a fruit cup is normally distributed with mean grams and standard deviation o grams. The weight of strawberries and blue berries are independent, and it is known that the weight of a fruit cup with average of 300 grams and standard deviation of 15 grams. 2 >> 2 (a) Find the values of u and o. botu=300 (b) The weights of the middle 96.6% of fruit cups are between (300K, 300+ K) grams. Find the value of K. (c) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. Find the values of L1 and L2 Question 2 (20 marks) A factory produces cylindrical metal bar. The production process can be modeled by normal distribution with mean length of 11 cm and standard deviation of 0.25 cm. (a) What is the probability that a randomly selected cylindrical metal bar has a length longer than 10.5 cm? (b) There is 14% chance that a randomly selected cylindrical metal bar has a length longer than K. What is the value of K? () The production cost of a metal bar is $80 per cm plus a basic cost of $100. Find the mean, median, standard deviation, variance, and 86 percentile of the production cost of a metal bar. (d) Write a short paragraph (about 30 - 50 words) to summarize the production cost of a metal bar. (The summary needs to include all summary statistics found in part (c)). (c) In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000, the senior manager decides to adjust the production process of the metal bar. The mean length is fixed and can't be changed while the standard deviation can be adjusted. Should the process standard deviation be adjusted to (1) a higher level than 0.25 cm, or (II) a lower level than 0.25 cm? (Write down your suggestion, no explanation is needed in part (e)).