Could someone kindly help me with steps to answering these questionsI would prefer if the solutions were on paper

For questions 1-6 refer to the following situation: A machine produces bottle caps. The machine is calibrated to produce bottle caps with a mean diameter of 2.8 cm and standard deviation of 0.03 cm. Let X represent the random variable for diameter of bottle caps. Leave your answers as a percent without rounding. [1 mark each] 1. What percent of bottle caps are between 2.77 cm and 2.83 cm? 2. Find P(2.74 5 x $ 2.86) 3. What percent of bottle caps are less than 2.71 cm? 4. Find P(x 2 2.86). 5. What percent of bottle caps are exactly 2.8 cm? 6. If all caps that are smaller than 2.71 cm and greater than 2.89 cm are rejected/thrown out, what percent would be lost? For questions 7-8 refer to the following situation: A men's shoe designer is willing to accommodate 95% of the male population. If the mean foot length is 25.25 cm and the standard deviation is 3.875 cm, answer the following: [1 mark each] 7. What is the smallest foot length the designed is willing to accommodate? 8. What is the largest foot length the designed is willing to accommodate? 9. Giselle is 168 cm tall. In her high school, boys' heights are normally distributed with a mean of 174 cm and a standard deviation of 6 cm. What is the probability that the first boy Giselle meets at school tomorrow will be taller than she is? [1 mark] MDM 4U Lesson 18 Assignment_ 21 Name PART B FULL SOLUTION. Write complete solutions in order to get full marks. You may sketch a normal curve for each case to help you with the answer 1 1) For Major League Baseball players, the mean of 432 batting averages is 0.261 with a standard deviation of 0.034. Suppose that the distribution is normally distributed. [2 marks each] a) Sketch a normal curve for this distribution of batting averages. Label the points that are 1. 2, and 3 standard deviations from the mean. b) What percent of batting averages are between 0.261 and 0.329? c) What percent of batting averages are less than 0.227? MDM 4U Lesson 18 Assignment 21 Name: 3. The vocabulary scores for seventh-graders in Indiana are normally distributed with a mean of 6.84 and a standard deviation of 1.55. a) Sketch a normal curve for this distribution of vocabulary scores. Label the points that are 1, 2, and 3 standard deviations from the mean