Application forms to a planning authority are not always filled out correctly. S

Question

Application forms to a planning authority are not always filled out correctly. Studies in a particular office show that during a six month period 10% of forms had to be returned to the applicants for correct completion. One hundred application forms are selected at random to determine the number of applications that needed to be returned.

i. State the random variable.

ii. Using the statistical tables, find the probability that:

A. More than fifteen applications have to be returned;

B. At least ten applications have to be returned;

C. Between eight and twelve (inclusive) applications have to be returned.

Explanation / Answer

(i) Here X is the random variable, representing the number of applications that are returned out of the 100 applications.

(ii) a) Probability that more than fifteen applications have to be returned is computed as:

= 1 - Bin(15,100,0.1)

= 1- 0.9601

= 0.0399

Therefore 0.0399 is the required probability here.

b) Probability that at least 10 applications have to be returned is computed as:

= P( X > =10) = 1 -P(X< =9)

= 1 - Bin(9,100,0.1)

= 1 - 0.4513

= 0.5487

Therefore 0.5487 is the required probability here.

c) Probability that Between eight and twelve (inclusive) applications have to be returned is computed as:

P( 8 < = X < = 12) = P(X < =12 ) - P(X < = 7)

= Bin(12,100,0.1) - Bin( 7,100,0.1)

= 0.8018 - 0.2061

= 0.5957

Therefore 0.5957 is the required probability here.

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