Question

34. MAT scores are approximately normally distributed with a mean of 547 and a standard deviation of 95. Estimate the percentage of scores that were(a) between 262 and 832. %(b) above 737. %(c) below 262. %(d) between 452 and 737. %

Answer 1

with the question given above,

(a) P(262= P[z < (832 - 475)/85] - P[z < (262 - 574)/95]

= P(z<3) - P(z<-3)

looking at the z-score table, we find

= 0.9987 - 0.0013

= 0.9973

= 99.7%

(b) P(x>737) = 1 - P(x <=737

= 1 - P[z<= (737 - 547)/95]

= 1 - P(z<= 2)

= 1 - 0.97725

= 0.02275

= 2.3%

(c) P(x < 262) = P(z< -3

= 0.0013

= 0.13%

(d) P(452= 0.97725 - P[z < (452 - 547)/95

= 0.97725 - P(z<-1)

= 0.97725 - 0.15866

= 0.81859

= 81.9%