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

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scores are normally distributed with an average score of 500 for
all U.S. students . A random sample of 100 students entering
Whitmer College had an average SAT Math (SAT-M) score of 475 and a
sample standard deviation of 120. The sample data can be used to
test the claim that the mean SAT-M score of all Whitmer College
students is lower than the national mean SAT-M score. Based...

For all U.S. students nationally who take the SAT, SAT Math
scores are normally distributed with an average score of 500 for
all U.S. students . A random sample of 100 students entering
Whitmer College had an average SAT Math (SAT-M) score of 520 and a
sample standard deviation of 120. The sample data can be used to
test the claim that the mean SAT-M score of all Whitmer College
students is higher than the national mean SAT-M score. Based...

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