Question

With this problem not use a computer software to solve it

A box contains 18 small items of various lengths. The lengths of the objects are 3 cm, 3 cm, 3 cm, 3 cm, 4 cm, 6 cm, 6 cm, 6 cm, 8 cm, 8 cm, 8 cm, 8 cm, 9 cm, 9 cm, 9 cm, 11 cm, 11 cm, and 11 cm.

(a) What is the probability that an object chosen at random from the box will have length 8 cm, assuming there is an equal probability of selecting any one object?

(b) What is the average length 〈?〉 (also called the expectation value of the length) of an object in the box?

(c) What is the probability that an object chosen at random from the box will have length 〈?〉, assuming there is an equal probability of selecting any one object?

(d) What is the average of the square of the length 〈? 2 〉 of an object in the box?

Answer 1

Hi,

Hope you are doing well.

Given that box contain 18 objects.

Sample space of given experiment, S={3,4,6,9,11}

(a)

Probability that an object chosen at random from the box will have length 8 cm= P(8)=

No.of events for getting object with length 8 cm=4

Total possible outcomes= 18

(b)

Average length (L)=

(c)

Probability that an object chosen at random from the box will have length (L)= P(L)= P(7)=

(d)

First of all lets find square of the length of every object in the box.

ie; 9 cm, 9 cm, 9 cm, 9 cm, 16 cm, 36cm, 36cm, 36cm, 64 cm, 64 cm, 64 cm, 64 cm, 81cm, 81cm, 81cm, 121 cm, 121 cm, 121 cm.

Average of the square of the length of an object in the box (?2)=

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