Question

In a certain state the recent average critical reading standardized test score was 481. Assume that the standard deviation is 50 and that standardized test scores are Normally distributed. Include an appropriately labeled and shaded Normal curve for each part. Complete

Include a Normal curve for each part.

a. What percentage of standardized test takers scored between 400 and 500? _______

b. What percentage of standardized test takers scored between 500 and 600? _______

Answer 1

a) P(400 < X < 500)

= P((400 - )/ < (X - )/ < (500 - )/)

= P((400 - 481)/50 < Z < (500 - 481)/50)

= P(-1.62 < Z < 0.38)

= P(Z < 0.38) - P(Z < -1.62)

= 0.6480 - 0.0526

= 0.5954

= 59.54%

b) P(500 < X < 600)

= P((500 - )/ < (X - )/ < (600 - )/)

= P((500 - 481)/50 < Z < (600 - 481)/50)

= P(0.38 < Z < 2.38)

= P(Z < 2.38) - P(Z < 0.38)

= 0.9913 - 0.6480

= 0.3433

= 34.33%