Answer all the questions

Question 7 The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 5 ounces. .Question 13 percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. Use the Empirical Rule. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 256 feet and a standard deviation of 41 feet. (a) Find the z-score corresponding to 45 percent of fat calories, rounded to 3 decimal places. Suggestion: sketch the distribution in order to answer these questions. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. (b) Find the probability that the percent of fat calories a person consumes is more than 45. a) 68% of the widget weights lie between and than 204 feet? a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer P(fewer than 204 feet) = (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use b) What percentage of the widget weights lie between 45 and 60 ounces? your z-score from part (a), rounded to one decimal place). than 216 feet? b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled more Shade: Left of a value B . Click and drag the arrows to adjust the values c) What percentage of the widget weights lie above 40 ? P(more than 216 feet) = Question 8 . Question 14 The time it takes me to wash the dishes is uniformly distributed between 12 minutes and 20 minutes. IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is 3 2 1 randomly chosen. Let X = IQ of an individual. What is the probability that washing dishes tonight will take me between 16 and 19 minutes? (a) Find the z-score for an IQ of 122, rounded to three decimal places. Give your answer accurate to two decimal places. (d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 (b) Find the probability that the person has an IQ greater than 122. decimal places. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use (e) Sketch the graph and write the probability statement. your z-score from part (a), rounded to one decimal place). Edit - Insert . Formats . B / U x X A A . Question 11 Shade: Left of a value . Click and drag the arrows to adjust the values. MyOpenMath it the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. If the area to the left of z in a normal distribution is 0.684, what is the area to the right of a? (a) In words, define the random variable X. Edit - Insert * Formats . B / U X X A A . Answer: -3 2 1 If the area to the right of a in a normal distribution is 0.684, what is the area to the left of a? 1.5 Answer: (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Question 12 (e) Sketch the graph, and write the probability statement. (b) Find the z-score for a trial lasting 13 days. (Round your answer to three decimal places.) A variable is normally distributed with mean 21 and standard deviation 9. Use your graphing calculator to fir Edit . Insert Formats . B I U x x A A (c) If one of the trials is randomly chosen, find the probability that it lasted at least 13 days. each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use a) Find the area to the left of 24. your z-score from part (b), rounded to one decimal place). (f) The middle 50% of IQs fall between what two values? b) Find the area to the left of 15. Shade: Left of a value B . Click and drag the arrows to adjust the values. c) Find the area to the right of 21. (g) Sketch the graph and write the probability statement. d) Find the area to the right of 25. e) Find the area between 15 and 30. Edit * Insert Formats . B I U x x A . A 2 1.5 (e) fifty percent of all trials of this type are completed within how many days