WorksheetsSampling Distribution
Total questions: 10
Worksheet time: 17mins
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 (a) .
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) .
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)
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.)
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).
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) (give as decimal)
(a)
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) .
(a)
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) .
(a)
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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