Question

Q4 i) A particular brand of sanitiser comes in three sizes: 25 ml, 40 ml, and 65 ml. 20% of all
purchasers select a 25ml bottle, 50% select 40 ml bottle and the remaining select a 65 ml
bottle. Let Xi and X2 be the bottle sizes selected by two independently selected
customers. Determine the sampling distribution of X. Calculate E (X) and compare it to u.​

Answer 1

Answer:

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Answer 2

Concept:

A probability distribution is a statistical function that specifies all of the potential values and probabilities for a random variable within a particular range. A probability distribution specifies the likelihood of an unknown value for a random variable. Random variables might be discrete, continuous, or a combination of the two.

Find:

The sampling distribution of X.

The value of E(X).

Solution:

The sampling distribution is

$P(X_1=25ml)=\frac{1}{5}\\\\P(X_2=40ml)=\frac{1}{2}\\\\P(X_3=65ml)=\frac{3}{10}$

The value of $E(X)=\sum_{i=1}^{n}x_iP(x_i)$

$E(X)=0.2*25+0.5*40+0.3*65\\E(X)=44.5$

Hence, the value of $E(X)$ is $44.5$.

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