KULULIVII Z IS PUILy Candy Bar Weights Exercise 12-10 asked you to assume that the actual weight of a certain candy bar, whose advertised weight is 2.13 ounces, varies according to a normal distribution with mean u = 2. 20 ounces and standard deviation O = 0. 04 ounces. a. What is the probability that an individual candy bar weighs between 2.18 and 2.22 ounces? Round your answer to 4 decimal places. A 7:59 PM 59 F O 4/13/2022 22 Mostly cloudy DELLQuestion 2 (1 point) b. Suppose you plan to take a sample of five candy bars and calculate the sample mean weight. Does the CLT apply in this instance? Explain. Yes, the CLT applies because the sample size n = 5 is considered large enough for any distribution. However, we need to assume the sample was taken randomly Yes, the CLT applies because the population is normally distributed, so sample size and random sampling both don't matter. 7:59 PM 22 59 F O 4/13/2022 Mostly cloudy DELL F12 PrtScr insert Delete F7 F8 F9 F10 F11 ES: F3 F4 F5 F6 O ESC F1 F2 140 BackspaceYes, the CLT applies because the population is normally distributed, so sample size doesn't matter. However, we need to assume the sample was taken randomly No, the CLT does not apply because the sample size is n = 5, which is too small No, the CLT does not apply because the population is normal 8:00 PM 59.F O 4/13/2022 22 Mostly cloudy DELL Insert Delete F8 F9 F10 F11 F12 PrtSer FS F6 F7 ESC F1 F2 F3 F4 144 X Backspace &he Sample means will be normally distributed 7 round your answers to 4 decimal places, if nece'r 33." f the sampling distribution. Shade in the re ,' the probability that the sample mean weigh 2.13 2.15 2.16 2.18 2.20 2.22 2.24 2.25 2.27 Mean Candy Bar Weight (in ounces) 8:01 PM 59 F O 4/13/2022 22 Mostly cloudy DELL Delete F11 F12 PriSer Insert F6 F7 F8 Fg F10 E'S: F4 O ESC F1 F2 F3 F5 144 Backspace2.08 2.08 2.09 2.11 2.13 2.15 2.17 2.18 2.20 8:01 PM 59 F O 4/13/2022 22 Mostly cloudy DELL Insert Delete FO F10 F11 PriScr F5 F6 F7 F8 F3 F4 ESC /F1 (F2 MX Back2.04 2.08 2.12 2.18 2.20 2.24 2.28 2.32 2.38 8:01 PM 59 F O 4/13/2022 22 Mostly cloudy DELL insert Delete FO F10 F11 F12 PrtSer F4 F5 F6 F7 F8 F3 ESC F1 F2 KK DII Backspace\fQuestion 5 (1 point) e. Use the Standard Normal Probabilities table or technology to calculate the probability that the sample mean weight of these five candy bars falls between 2.18 and 2.22 ounces. Probability = ___ (round to 4 decimal places) A 8:03 PM 4/13/2022 22 59.F Mostly cloudy DELL Insert Delete F11 F12 Priser CO =10 F6 F7 F4 F5 F2 F3 144 ESC ( F1 Backspa $ % @ 6 3 4 5 2f. How do you expect this probability to change if the sample size were 40 instead of 5? Explain your reasoning. The probability will decrease if the sample size increases to 40, because this will increase the standard deviation, meaning less of the data is concentrated near center. O The probability will decrease if the sample size increases to 40, because this will decrease the standard deviation, meaning less of the data is concentrated near center. 8:03 PM 22 59.F O 4/13/2022 Mostly cloudy DELL PrtSer Delete F12 Insert F8 FO F10 F11 F7 F4 F5 F6 F2 F3 ESC X Backspace $ % aO The probability will increase if the sample size increases to 40, because this will decrease the standard deviation, meaning more of the data is concentrated near center. The probability will increase if the sample size increases to 40, because this will increase the standard deviation, meaning more of the data is concentrated near center. 8:03 PM 4/13/2022 22 59.F O Mostly cloudy DELL Insert Delete F11 F12 Prtser F8 FO F10 F4 F5 F6 O ESC F1 F2 F3 144 Backspa & $ O 7 5 6 2 3 4 O P T Y UQuestion 7 (1 point) g. Calculate this probability that the sample mean is between 2.18 and 2.22 for a sample size of 40 and determine if your guess in part f was correct. Round your standard deviation and your probability to 4 decimal places. A/ 8:03 PM 4/13/2022 22 59. F Mostly cloudy DELL F12 PrtScr insert Delete F9 F11 F5 F6 F7 F8 F10 O F1 F2 F3 F4 ESC X Backspa & @ # $ O 7 4 5 2 3h. Which of your previous calculations (parts a, e, and g) remain approximately correct even if the candy bar weights themselves have a skewed, non-normal distribution? The calculations in e and g remain correct O All three calculations remain correct The calculations in a and g remain correct 8:04 PM 59.F O BAROONO 4/13/2022 22 Mostly cloudy DELL F11 F12 PrtSer insert Delete F10 F4 F5 F8 FO F6 F7 Esc F1 F2 F3 & K Backs