Question

According to the z distribution, what proportion of GRE verbal scores would fall between 400 and 696?

.3413

.4750

.8163

.1683

Answer 1

SOLUTION:

From given data,

According to the z distribution, what proportion of GRE verbal scores would fall between 400 and 696?

proportion of GRE verbal scores would fall between 400 and 696

Let x : GRE verbal score

Let us consider,

mean = = 500

Standard deviation = = 100

Let x Normal ( = 500 , = 100)

Z = (x-) / = (x-500) / 100

P(400 < X < 696) = P( (400-500) / 100 < (x-500) / 100 < (696-500) / 100 )

P(400 < X < 696) = P(-100/ 100​​​​​​​ < Z < 196 / 100 )

P(400 < X < 696) = P(-1 < Z < 1.96)

P(400 < X < 696) = P(Z < 1.96) - P(Z < -1)

Where,

[ P ( Z<−1 ) can be found by using the following formula.

P ( Z<−a)=1−P ( Z<a )

After substituting a=1 we have: P ( Z<−1)=1−P ( Z<1 ) ]

P ( Z<−1)=1−P ( Z<1 )=1−0.8413=0.1587

P ( Z<1.96 ) = 0.975.

Now,

P(400 < X < 696) = 0.975 - 0.1587 (from z score table)

P(400 < X < 696) = 0.8163

Answer : 3rd option is correct.