Sampling Distribution

Note that questions 2 - 6 use one data set, and questions 7 - 9 use another data set, so you don't have to keep calculating from scratch.

All the questions and your answers will be shown at the end / bottom of the last screen, so you can take a screen grab for reference after the quiz.

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The masses of Brand A and Brand B of a tin of cookies, in kg, have normal distributions N(3, 0.8) and N(2, 0.5) respectively.

I bought 10 tins of A.   The total mass has variance ____ .

The masses of Brand A and Brand B of a tin of cookies, in kg, have normal distributions N(3, 0.8) and N(2, 0.5) respectively.

I bought 10 tins of A.   The average mass has variance ____ .

The masses of Brand A and Brand B of a tin of cookies, in kg, have normal distributions N(3, 0.8) and N(2, 0.5) respectively.

I bought three tins of A and two tins of B.   The total mass has variance ____ (give as exact decimal answer)

The masses of Brand A and Brand B of a tin of cookies, in kg, have normal distributions N(3, 0.8) and N(2, 0.5) respectively.

I bought three tins of A and two tins of B.   The average mass has variance ____  (give as exact decimal ans.)

The masses of Brand A and Brand B of a tin of cookies, in kg, have normal distributions N(3, 0.8) and N(2, 0.5) respectively.   Each kg of A costs $3, each kg of B costs $4.

I bought three tins of A and two tins of B.   The total COST has variance ____ (as a decimal).

The discrete random variable X has probability distribution
P(X = 4) = 0.75, P(X = 8) = 0.25.
X_1 and X_2 are independent observations of X.
Find  $P\left(X_1+X_2\le13\right)$  (give as decimal)

The discrete random variable X has probability distribution
P(X = 4) = 0.75, P(X = 8) = 0.25.
X_1, X_2, ..., X_60 are independent observations of X.
Estimate the value (correct to 3 s.f.) of  $P\left(X_1+X_2+X_3+...+X_{60}\le308\right)$ . 

The discrete random variable X has probability distribution
P(X = 4) = 0.75, P(X = 8) = 0.25.
A is the average of 70 independent observations of X.
Estimate the value (correct to 3 s.f.) of  $P\left(A\le4.9\right)$ . 

In short, in this topic, it's important to understand a few ideas:

1) How to obtain mean and variance, ie. derive the variance using what you learnt in the previous chapter, don't just memorise [Var(X) / n] and anyhow apply even when it's wrong to do so.

2) Know when you can apply Central Limit Theorem --- it's not about the mean and variance computation, but mainly about when a distribution is approximately normal. When the theorem is not applicable, you have to go back to concepts and methods in earlier chapters.

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