Final answer:
The percentage of scores between the mean and a Z score of 2.14 is 98.42%, the percentage of scores above 2.14 is 1.68%, and the percentage of scores below 2.14 is also 1.68%.
Step-by-step explanation:
The percentage of scores between the mean and a Z score of 2.14 can be found using the normal curve table. The area under the normal curve between the mean and a Z score of 2.14 is the same as the area between the mean and a Z score of -2.14. Using the normal curve table, we can find that this area is approximately 0.9842. To find the percentage, we can multiply this by 100, giving us 98.42%.
The percentage of scores above 2.14 can be found by subtracting the area to the left of 2.14 from 1. The area to the left of 2.14 is approximately 0.9832, so the area above 2.14 is 1 - 0.9832 = 0.0168. Multiplying this by 100 gives us 1.68%.
The percentage of scores below 2.14 is the same as the percentage of scores above -2.14, which we just found to be 1.68%. So, the answer is (b) (a) 13.59%, (b) 86.41%, (c) 13.59%.