Question

A research found that 45% of Wawasan College’s students used mobile phone. If a sample of 200 students is selected at random, find the probability of the proportion of students used a mobile phone are less than 80?

Answer 1

let X be a student of wawasan college's use a mobile phone.

now the probability that a student uses a mobile phone is P = 0.45, so Q = 1 - P = 1 - 0.45 = 0.65

Thus if a sample of n = 200 students is selected at random.

X follows binomial distribution

i.e  

now here n=200 which is too large, so we will use normal approximation

so mean = n * p = 200 * 0.45 = 90

Thus,

so, to find P(X<80)

        this is becuase of the symmetry of the distribution.

now look we will find the probabilities from the table given below.

so to find the P(Z<1.4213)

look in the table for 1.4 the 1st column and 0.02 in the 1st row.

the value is 0.9222.

P(Z<1.4213) = 0.9222

thus,

P(Z<-1.4213) = 1 - 0.9222

P(Z<-1.4213) = 0.0778

Hence, probability that of the proportion of the students used mobile phone are less than 80 is 0.0778.

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