probability question The standard normal Z table at httpwwws

probability question

The standard normal (Z) table at http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm contains, for each value of Z from 0 to about 3, the area under the standard normal curve N(0, 1) to the left of x = Z. As discussed in class, this area can be interpreted as the probability that a value selected at random from the standard normal distribution (mean µ = 0, standard deviation = 1) will be less than or equal to Z. Using only this table and the fact that any normal distribution N(µ, ) is a rescaling of the standard normal distribution, answer the following questions.

Question: Look at the table of 2013 SAT score percentiles at

http://media.collegeboard.com/digitalServices/pdf/research/SAT-Percentile-Ranks-2013.pdf

Based on this table, assuming that no further re-centering or re-norming of scores has taken place since 1995, have students as a whole become better or worse at taking the test? Which section is currently “harder”: math or verbal? Justify your answers in light of the data in the table.

show your work!

Solution

ASSUME

z=1.25

then P(z<1.25 ) = 0.5+ P(0<Z<1.25) =0.5 + 0.3944 =0.8944 (from normal tables)