Question

We believe that 70% of the population of all statistical methods one students considers statistics and exciting subjects suppose we randomly and independently selected 1000 students from the population now we want to find the probability of observing 700 or more students who consider statistics to be an exciting subject in our sample of 1000 students

Find the value of the variable X

Find the variance of the variable X

find the probability of observing 700 or more students who consider statistics to be an exciting subject in our sample of 1000 students

Answer 1

Given that 70 y. Of the population of au statistical method one students considers statistics as an exciting subject. Hence the poobability that a randomly selected student considers statistics as an exciting Subject=0.70 Let x be the number of students ; Out Of 100m selected randomly; considers Statistics an exciting subject. Then x fullocos Binomial distoi- bution with n= 1000 and p= 0.70 variance 210 Expected value of x = n*P = 1000 *0-70= 700 van'ance Of X n**(1-p) = 1000*0.70*0.30= 210 AS n* p = 700 and n* (-p) = 300 are greater than 5; we can use normal appoorimation to Binomial to find the probabilities corresponding to different values of x. x is approximately normal with mean u = 700 and standard deviation on = 14.49 We need to calculate the poobability that 700 or more students observing Statistics to be an exciting subject ie PCX 2700). Before applying the normal apparatimation we need to do cordurinty correction on the value of xa8 bmorial is a discrete distribution and normal is a continuous distribution. continuity corrections for p (x 2a) is pcx>0-0.5) Hence PCX 2700) = P(x > 700-0.5) = P(x>699.5) Now z score for 699.5 is 699.5-M 699.5-700 74-49 fy-0.03 : P(x > 699.5) - PC2>-0.03) - Area to the right of -0.08 under the standard normal curve = |- Area to the left of -0-03 = 1-0.4880 = 0-512 poobability of observing 700 or more students who consider Stahstics to be an ercting subject in the sample of 1000 students = 0.512