Question

(4) 1. SAT math scores are normally distributed with a mean 525 and a standard deviation of 102. In order to qualify for a college you are interested in attending your SAT math score must be in the highest 9.34% of all SAT scores. What is the minimum score you need on the SAT to qualify for the college?

(4) 2. If you get into this college you are interested in running for the track team. To qualify for the track team you must run in the fastest 4.75% of all runners of the mile. If the running of the mile is normally distributed with a mean of 6.02 minutes and a standard deviation of 1.32 minutes what is the maximum time you have to run the mile and still qualify for the team?

Answer 1

Solution:-

Given that,

mean = = 525

standard deviation = = 102

Using standard normal table,

P(Z > z) = 9.34%

= 1 - P(Z < z) = 0.0934  

= P(Z < z) = 1 - 0.0934

= P(Z < z ) = 0.9066

= P(Z < 1.32 ) = 0.9066

z =1.32

Using z-score formula,

x = z * +

x = 1.32 * 102+525

x = 659.64

x=660

(4)

Solution:-

Given that,

mean = = 6.02

standard deviation = = 1.32

Using standard normal table,

P(Z > z) = 4.75%

= 1 - P(Z < z) = 0.0475

= P(Z < z) = 1 - 0.0475

= P(Z < z ) = 0.9525

= P(Z <1.67 ) = 0.9525

z =1.67

Using z-score formula,

x = z * +

x = 1.67* 1.32+6.02

x = 8.22 minutes