Question

From the college records, It was always known that 10% of the students who take Eng. 304 course would receive a letter grade of an "A", among the lo sections of the same course which usually total to 350 students, . Using the normal approximation concept, please find the following: 1. Probability that at least 40 students will receive A's? 2. Probability that at most 300 students will receive grades other than A's? 3. Expected number of students and the variance for those who will receive A's.?

Answer 1

Consider the binomial distribution with = 350 , p = 400, South 5.61 of follows normal distribution with u = np = 35 and o= ſupq = √3115 a 5.61 :: Z = X = X-35 follows Mandand normal distribution (). The required probabilitý corresponds:. 339.5-4 = P(Z > 39.5-35) - P(Z 70.807) 1-0.79389; = 0.20611 applied correction rules to 40 to get 39.5) (2). 350 – 300 = 50, (Here we have consider almost í are 50 students get The required probability 49.5-35) = P(77 Jalis -35) = P(Z > 2.584) = I= P(Z < 2.584) = 1-0.99506 = 0.00494 (3). Expected value = x= 35 Variance =02= npq = 31.5