In a class on advanced water buffalo husbandry, the midterm exam raw scores (i. e., the values of x) form a normal distribution, with a mean of 239 and a standard deviation of 37. 6) [5 pts.] what percentage of exam scores are more than 1.5 standard deviations of distance away from the mean? 7) [5 pts.] what proportion of students had an exam score between 180 and 250? 8) [5 pts.] 20% of the students had an exam score that was higher than what value? 9) [5 pts.] which exam score corresponds to the 67th percentile?

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.