Question

The mathematics section of a standardized college entrance exam had a mean of 19.819.8 and an SD of 5.25.2 for a recent year. Assume these are well modeled by a Normal distribution.

a) About what percent of students scored over 29​?

​b) About what percent of students scored under 14​?

​c) About what percent of students scored between 14 and 29​?

Answer 1

Solution :

Given that,

mean = = 19.8

standard deviation = = 5.2

a ) P (x > 29)

= 1 - P (x < 29 )

= 1 - P ( x -  / ) < ( 29 - 19.8/ 5.2)

= 1 - P ( z < 9.2 / 5.2 )

= 1 - P ( z < 1.77 )

Using z table

= 1 - 0.9616

= 0.0384

Probability = 0.0384 =3.84%

b ) P( x < 14 )

P ( x - / ) < ( 14 -19.8 / 5.2)

P ( z < - 5.8 / 5.2 )

P ( z < -1.11)

= 0.1335

Probability = 0.1335 =13.35%

c ) P (14 < x < 331 )

P ( 14- 19.8 / 27) < ( x -  / ) < ( 29 - 19.8 / 5.2)

P ( - 5.8 / 5.2 < z < 9.2 / 5.2 )

P (-1.11 < z < 1.77)

P ( z < 1.77 ) - P ( z < -1.11)

Using z table

= 0.9616 - 0.1335

= 0.8281

Probability = 0.8281 = 82.81%