Question

Exercise 5. (20pts) High School Competency Test A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. (5a) (10pts) The top 4% of students receive $500. What is the minimum score you would need to receive this award?. Draw a picture (5b) (10pts) The bottom 2% of students must go to summer school. What is the minimum score you would need to stay out of this group?.Draw a picture

Answer 1

Given that,

mean = = 400

standard deviation = =100

Using standard normal table,

P(Z > z) = 4%

= 1 - P(Z < z) = 0.04

= P(Z < z ) = 1 - 0.04

= P(Z < z ) = 0.96

z =1.75 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.75 *100+400

x= 575

b

P(Z < z) = 2%

= P(Z < z) = 0.02

= P(Z <2.05 ) = 0.98

z = 2.05 Using standard normal z table,

Using z-score formula  

x= z * +

x=2.05 *100+400

x= 605