Question

The probability that a student is admitted to University of Nizwa is 0.3 . A random sample of 5 students from the same school has applied What is the probability that ( 1 ) at most 2 are accepted ? ( ii ) at least 3 are rejected ?

Answer 1

1)

The population proportion of success is p = 0.3, also, 1 - p = 1 - 0.3 = 0.7

, and the sample size is n= 5.

We need to compute Pr [Atmost 2 are accepted] = Pr(X≤2)

Therefore, we get that

This implies that

2)

Pr[ student is rejected] = 1 - 0.3 = 0.7

The population proportion of success is p = 0.7, also, 1 - p = 1 - 0.7 = 0.3

and the sample size is n= 5.

We need to compute Pr(X≥3)

Therefore, we get that

This implies that

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