Hi, please I need a help with this statistics and data analysis questions.

Part 1

A group of amateur bowlers goes to a tournament. The distributoion of scores was found to be approximately normal: N(198, 16), i.e. mean of 198 and standard deviation of 16.

Important: For this problem, I do not expect you to come up with accurate answers, but I DO want you to be in the vague ballpark. For example, if some observation has a value that is just below the mean, do not report a quantity of greater than 50%! Instead, you should say: "Just below 50%". Also, if for any of your answers you expect the result to be "very very low" or "very very high", you can simply say so. That is, do not feel the need to specify a number.

1. About what percentage of the bowlers had a result LOWER than 198?
2. About what percentage of the bowlers had a result HIGHER than 214?
3. About what percentage of the bowlers had a result LOWER than 162?
4. About what percentage of the bowlers had a result HIGHER than 182?
5. About what percentage of the bowlers had a result HIGHER than 197?

Note:

• In all cases, be sure to explain your reasoning.
• While you DEFINITELY should draw these out when doing the problems, you are not required to include those drawings in your assignment.

For part 2 questions I only need help with question number 3 and 4. Thank you in advance for your help.

A manufacturing line wants to analyse their production. They begin by looking at the number of products that were produced over the previous 100 days.

Here are the results. Note that they are not sorted.

760, 796, 869, 811, 789, 838, 801, 810, 837, 837, 858, 791, 806, 831, 776, 822, 801, 828, 830, 815, 819, 841, 827, 797, 843, 857, 814, 839, 821, 829, 798, 823, 784, 855, 848, 818, 852, 808, 803, 803, 836, 876, 808, 856, 843, 822, 821, 817, 841, 822, 824, 801, 806, 835, 794, 854, 802, 803, 813, 825, 839, 808, 816, 823, 779, 806, 770, 819, 817, 850, 808, 783, 872, 824, 804, 819, 808, 816, 807, 857, 781, 850, 822, 811, 778, 844, 792, 807, 794, 802, 777, 777, 819, 815, 805, 810, 782, 833, 819, 764

1. Paste this into a vector, and print a histogram.
2. Using R, summarize the variable by calculating the descriptive statistics including mean, SD, 5-number summary, and boxplot.
3. Calculate the z-score for the lowest and highest values in the group. Hint: You should NOT need to visually go through the list to determine the highest and lowest values. Look at the various statistics you have already obtained from R. Answer to two decimal places.
4. How many products would be produced with a z-score of 3?