The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. a. What is the distribution of X? X ~ N(:],[:]) b. Find the probability that a randomly selected person with a kidney stone will take longer than 8 days to pass it. Round to 4 decimal places. [j Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N([:],[:]) b. If one of the trials is randomly chosen, find the probability that it lasted at least 12 days. [:1 c. If one of the trials is randomly chosen, find the probability that it lasted between 18 and 21 days. [:1 The time to complete an exam is approximately Normal with a mean of 45 minutes and a standard deviation of 9 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes. u- 30 .ui-ZO |.I.- O p.+0 p.+20 p.+30 The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 45 ounces and a standard deviation of 11 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between and _ b) What percentage of the widget weights lie between 12 and 67 ounces? % c) What percentage of the widget weights lie above 34 ? % .-. a. n