Normal Distribution and Errors in Measurement Watch the following video (the first two minutes is all you need to watch): [LINK] [+] Whenever a quantity (volume, mass, time, etc.) is measured, there is always some uncertainty about the exact amount. This creates variation in the measurements. Suppose a machine fills bottles with soda. Each bottle is labeled "500 mL". However, because of variations in measurement, each bottle does not contain exactly 500 mL of soda. Suppose the true distribution of the volume of soda in each bottle is normally distributed with a mean of 500.0 mL and a standard deviation of 0.4 mL. In the textbox below, answer these questions: a) Draw the normal curve that represents the distribution of the volume of soda in each bottle. Label the x-axis with 1, 2, 3 standard deviations above and below the mean. Also, label the z-scores underneath. See this example of a normal curve ( = 60 , o = 5 45 50 60 65 70 :75 2 3. b) According to the 68-95-99.7 rule, 95% of the bottles will have between and mL of soda.Question 2 0/10 pts ) 4 0 Details If a bottle is chosen at random, what is the probability it has less than 499.5 mL of soda? a. Write the probability notation for this question, using X as the random variable b. draw the normal curve from question 1 and shade in the region that represents the probability. Then use the picture to estimate the probability (it does not have to be precise. Just a rough guess is fine) c. Convert 499.5 mL to a z-score, then write the probability notation, using Z as the random variable d. Draw the standard normal curve and shade the region that corresponds with the probability e. Use Statcrunch to find the probability. Do this twice: using X and then using Z. Take a screen shot of each (shift+command*4 on apple, window+shift+S on PCs) and paste it into the textbox below. Edit . Insert * Formats BIUXX ATA e Question Help: D Post to forum Submit QuestionQuestion 3 0/10 pts 9 4 0 Details Suppose another machine (Let's call this Machine B) also fills bottles with soda, and this time the mean volume is 500.0 mL and the standard deviation is 0.2 ml. . a. sketch a graph of the distribution, and include 3 standard deviations above and below the mean. b. According to the 68-95-99.7 rule, 95% of the bottles have between and mL of soda. c. Which machine is more accurate? Explain Edit * Insert * Formats BIUXX A A (> @ Question Help: D Post to forum Submit