A school board is considering creating a new mathematics program to help improve their students math skills.As a first step,they wish to find out how their students math skills compare to provincial standards.So,they administer a math test with all their Grades3-6students and discover that the distribution of scores is approximately normally distributed with mean105and standard deviation15.

a.The minimum provincial standard for this math skills test for Grades3-6students is70. Approximately what percentage of students in the district do not meet this provincial standard?

b.The school board has the resources to offer the new math program to the10%of their students who scored lowest on the literacy test.What score will represent the eligibility cut-off scorefor this new math program in the school district?

If someone could provide a detailed explanation (using probability terms and formulas) and a step by step solution, it will be greatly appreciated. Thank you