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Sampling Distribution

Total questions: 10

Worksheet time: 17mins

Name
Class
Date
1.

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.


You got these instructions?

a)

Yes

b)

No, I hate reading, Mr Ho.

2.

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 (a)   .

3.

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 (a)   .

4.

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 (a)   (give as exact decimal answer)

5.

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 (a)     (give as exact decimal ans.)

6.

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 (a)   (as a decimal).

7.

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(X1+X2≤13)P\left(X_1+X_2\le13\right)  (give as decimal)



(a)  

8.

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(X1+X2+X3+...+X60≤308)P\left(X_1+X_2+X_3+...+X_{60}\le308\right) . 



(a)  

9.

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(A≤4.9)P\left(A\le4.9\right) . 



(a)  

10.

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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