Question

2. Binomial Distribution In a high school yearbook, there are 200 pictures of students. John received five autographs from his friends. Suppose we randomly sample 100 students to see if John received an autograph from the students. Let X = the number of these students that John received an autograph. A) Find the mean and standard deviation B) Find the probability that we find between 3 and 4 students out of the 100 students have autographed John's year book.

Answer 1

Total photo graphs = goo No. of autographs recieved - 5 Now Pl auto graph recievel) = 5/800 = oogs so Wome P=0.025 Sample size S2 (n) = 100 Mean (4)= np Il = 100 x0.025 u= 2.5 ] . . standard deviation (6)= nechal r. sloo xo.oasx0.975 re 1.56] sample i l 2.5 and so mean of this standard deviation is 1:56

(1) 2( 32 244); Ž 10OC, (83" CT-Bjhe 1 *-3 . až 1096 (0.095)* (0-915) 100-) x=3 P(35x34) = 0.89373 – 0.75895 Ć 0.13478 Probability detween 3 8 u auto graphs is [ 0.13478) 읽