Question

Please show how to solve using excel.

At a large university, the mean age of the students is 22.3 years, and the standard deviation is 4 years. A random sample of 64 students is drawn. What is the probability that the average age of these students is greater than 23 years? In another large university, 25% of the students are over 21 years of age. In a sample of 400 students, what is the probability that more than 110 of them are over 21?

Answer 1

Central limit theorem :- It x have a dists with ean ll to Std dev 6 then for large n (n) 30) the suppling disth of sample mean (7) follows Normal dirth with mean it std dere ols). Ty lu, olin) M 2 = 22.3, 6-4, n=64 lx = 22.3 57 = ro - 418- 0.5 xt MC 1 2 = 22.3 7 Tour PC ) 23 ) = ? In Excel commeret for pcx srl = ... " NORM. DIST(x, mean, std deviation, Cumartes " PCT 223) - tobagobai forebror sort "MORM. DIST (23, 22.3, 0.5, 1) - 0.9192 40 . PCFL23) - 0.9192 down it PC7 > 23) - -PCX 423) 1~0.9192 = 0.0808 10.0808] - NORM. DIST(23, 22.3, 0.8 1) = 0ofos 2) x- method o n = 400, P=0.25 to X - Binomial (n=400, P=0.25) Mormal cepproni mation. Ect) = 1 - np = 100 6(+) = 6 - Inroup) = (hoor 0.2ixon - = 8-66 X Normal (ll = 100 6 8.66) 7

P ( X 3110) = ? In Excel " - MORM. DIST (110, 100,8.66, 1)? - 0.1241 10.1241 method 2:- Direet Binomial probability In Etrel Pct srl - BINOM DIST plumber, tricel, - Probasale, come P(x), 2) =) - Bonom.DIST. PCX5 110) - I-P(+ 5100) - BINOM. DIST (1lo, 600,0.25, 1) Oo 1130 011 10.11357

In q.2) firest we used normal approximation & in seconds method used exact binomial probability. so answer may vary.because first part is an approximation