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In a certain high school, historically 40% of graduates will go on to college. This the year graduating class has 120 students a) Find the expected value and standard deviation of the number of these graduates who will go on to college. b) The record number of graduates from a class who go on to college is 58. Using an appropriate approximate method, find the probability that this year's class will beat that record

Answer :

(a) The expected value is 48 and the standard deviation is 5.366  .

(b) The probability that this year's class will beat the record is 0.0250  .

In the question ,

it is given that ,

the number of students is (n) = 120

40% of graduates will go on to college , that means (p) = 0.4

Part(a)

the expected value is E(x) is

E(x) = n*p = 120*0.4 = 48 .

the standard deviation is √np(1-q) = √120*0.4*0.6 = √28.8 ≈ 5.366

Part(b)

Using normal distribution for approximation ,

μ = 48 , σ = √28.8 and z = (x - 48)/√28.8   .

P(class will beat the record) = P(x>58)

= P(x>58.5)    continuity correlation

= P(Z > (58.5 - 48)/√28.8) = P(Z > 1.96) that is

= 0.0250 .

Therefore , (a) expected value = 48 , standard deviation = 5.366

(b) the required probability is 0.0250  .

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