MS 150 Statistics Summer 2001 Quiz 3

The College Entrance TOEFL test has a mean m = 437 and a standard deviation s = 76.  This August the College will receive a Student Services and Support (SSS) grant from the United States Department of Education.  This grant will provide academic support including tutoring and academic counseling to incoming freshmen here at the national campus.  The target student are those who come in with weak math and English skills.

  1. What percent of the students will be between 470 and 530 on the TOEFL test?  That is, find the probability P(470<x<530).  Report the probability as a decimal or percent, your choice.

  2. If 300 freshmen are admitted, how many freshmen will be served by the SSS grant if we serve only students who score between 470 and 530 on the TOEFL?

  3. Using the same information on the mean and standard deviation given above, find the TOEFL score above which only 10% of the students scored.  That is, find P(x > ______) = 0.10.
Statistic Equations Excel
Mean = xbar.gif (842 bytes) = x P(x) =AVERAGE(data)
Sample Standard Deviation = sx
= sampstdev.gif (1072 bytes)
Population Standard Deviation = s
= probabilitypopstdev.gif (1053 bytes)
Slope =SLOPE(y data, x data)
Intercept =INTERCEPT(y data, x data)
Correlation =CORREL(y data, x data)
Find a probability from a z value =NORMSDIST(z)
Find a z value from a probability p =NORMSINV(p)

Excel calculates the probability from the "far left":

Standard normal cumulative distribution left to z: Excel functions