Suppose that the national average for the math portion of the college board’s sat is 515. the college board periodically rescales the test scores such that the standard deviation is approximately 100. answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. a. what percentage of students have an sat math score greater than 615? b. what percentage of students have an sat math score greater than 715? c. what percentage of students have an sat math score between 415 and 515? d. what is the z-score for student with an sat math score of 620? e. what is the z-score for a student with an sat math score of 405?

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?