Question

In 2017, the average ACT score a specific state was 19.5. If the standard deviation is 3, what percentage of people that took the ACT made between a 18-22?

Select one

a. 10%

b. 52%

c. 79%

d.48%

Answer 1

Solution :

Given that ,

mean = = 19.5

standard deviation = = 3

P( 18 < x < 22) = P[( 18 - 19.5 )/ 3 ) < (x - ) /  < ( 22 - 19.5 ) / 3 ) ]

= P( -0.5 < z < 0.83 )

= P(z < 0.8 ) - P(z < -0.5 )

Using z table

= 0.7881 - 0.3085

= 0.4796

The percentage is = 47.96% = 48% ( Round to nearest)

correct option is = d.