Question

It is possible to score higher than 16001600 on the combined mathematics and reading portions of the SAT, but scores 16001600 and above are reported as 1600.1600. Suppose the distribution of SAT scores (combining mathematics and reading) was approximately Normal with mean of 1021 and standard deviation of 214.214.

What proportion of SAT scores for the combined portions were reported as 1600?1600? That is, what proportion of SAT scores were actually higher than 1600?1600? (Enter an answer rounded to four decimal places.)

proportion above 1600=1600=

Answer 1

Solution:

We are given that scores are normally distributed.

Mean = 1021

SD = 214

We have to find P(X>1600)

P(X>1600) = 1 – P(X<1600)

Z = (X – mean) / SD

Z = (1600 - 1021)/214

Z = 2.705607

P(Z<2.705607) = P(X<1600) = 0.996591

(by using z-table or excel)

P(X>1600) = 1 – P(X<1600)

P(X>1600) = 1 – 0.996591

P(X>1600) = 0.003409

Required probability = 0.0034