Question

Scores on the SAT exam approximate a normal distribution with mean 500 and standard deviation of 80. USe the distribution to determine the following. (Z score must be rounded to two decimal places:

(a) The Z- score for a SAT of 380 (2pts)

(b) The percent of SAT scores that fall above 610 (3pts)

(c) The prpbability that sn SAT score falls below 720 (3pts)

(d) The percentage of SAT scores that fall between 470 and 620 (4pts)

Answer 1

Solution :

Given that,

mean = = 500

standard deviation = = 80

a ) x = 380

z =  X - /

= 380 - 500 / 80

= - 1.20 / 80

= - 1.5

The Z- score  = - 1.5

b ) P (x > 610)

= 1 - P (x < 610 )

= 1 - P ( x -  / ) < ( 610 - 500 / 80)

= 1 - P ( z < 110 / 80 )

= 1 - P ( z < 1.37 )

Using z table

= 1 -0.9147

= 0.0853

Probability =0.0853

C ) P( x < 720)

P ( x - / ) < ( 720 -500 / 80)

P ( z < 220 / 80 )

P ( z < 2.75 )

= 0.9970

Probability = 0.9970

d ) P (470 < x < 620 )

P ( 470 - 500 / 80) < ( x -  / ) < ( 620 - 500 / 80 )

P ( - 30 / 80 < z < 120 / 80 )

P (-037 < z < 1.5)

P ( z < 1.5 ) - P ( z < -037)

Using z table

= 0.9332 - 0.3557

= 0.5775

Probability = 0.5775