Question

Question 2. Suppose the scores on a college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100.

a) Find the probability that an individual scores below 400.

b) Find the probability that an individual scores 650 or higher.

c) A certain prestigious university will consider for admission only those applicants whose scores exceed the 93th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university.

Answer 1

solution :- Given :- Mean (el) = 55o. std devi (r) = 100 9 P(x < 400) = P (x- - el o 550 Too = P(Z <-115) = 0.0668 PC*<400) P ( x 7 650) = t - P ( x < 650) = 1- P(xace < 650-550) too i) = 1- P(Z < = 1 - 0.8413 P(X7, 650) = 0.1587 I formula, () The 'zi distribution of I - the 93 % is, 4 By using '2' score P(272) = 93% I-P(Z <=) = 0.93 x = 2 * r tu P(Z <2) = 1-0.93 x = (-1.476) * 100+550 P(Z < 2) = 0.07 X = 402.4 P(Z < -1.476) = 0.07 minimum score an applicant must 2 = -1.476 achieve for admission to the University is 402.4