Question

34. GMAT 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 452 and 642. %(b) above 832. %(c) below 452. %(d) between 357 and 832. %

Answer 1

(a) between 452 and 642%

P(452= P[z < (642-547)/95] - P[z < (452-547)/95]

= P(z<1) - P(z<-1)

looking at the z-score table, we have:

= 0.8413 - 0.1587

= 0.6826

= 68.26%

(b) above 832%

P(x > 832) = 1 - P(x <= 832)

= 1 - P[z<= (832-547)/95]

= 1 - P(z<=3)

= 1 - 0.9987

= 0.0013

= 0.13%

(c) = below 452%

P(x < 452)

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

= P(z < -1)

= 0.1587

= 15.87%

(d) P(357= P(x<832) - P(x<357)

= 0.9987 - P[z < (357 - 547)/95

= 0.9987 - P(z<-2)

= 0.9987 - 0.0228

= 0.9759

= 97.59%