Question

(5.12) A university that is better known for its basketball program than for its academic strength claims that 80% of it’s basketball players get degrees. An investigation examines the fate of all 20 players who entered the program over a period of several years that ended 5 years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the university’s claim is true, the number of players who graduate among the 20 studied should have the B(20, 0.8) distribution.

1. (a) Find the probability that exactly 11 players graduate under these assumptions. (Use software or normal approximation.)

2. (b) Find the probability that 11 or fewer players graduate. This probability is so small that it casts doubt on the university’s claim.

Answer 1

a) Gvennp=20p-0.8-16, npq= 20*0.8*0.2 = 3.2 The probabilihy that exactly 11 players graduate under these assurptions is P(X=11) =P(10.5 <X <115) 10.5-nP X-nP 11.5-nP 10.5-16 11.5-16 32 232 P (-3074598 Z <-251557) 3.2 = 0.00489 Using sofiware BINOM.DIST(11,20,0.8,FALSE) Result: 0.007387 b) the probability that 11 or jewer players graduate P(Xs11-P(X <11.5) X-nP 11.5-nP Since continuity correction 11.5-16 3.2 -P(Z <-2.51557) = 0.00594 Using Software BINOM.DIST(11,20,0.8,TRUE) Results.0.009982