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3.2 Finding Probabilities for Normal Distributions

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Question 1

An electronics engineer measures the resistance, $r$ ohms, of a specific component. The measured resistance, $X$ ohms, is normally distributed with mean $r$ ohms and standard deviation $0.8$ ohms.

Find the probability that $X$ is within $1.0$ ohm of $r$ .

[2]

The same component is measured 25 times and the results are recorded.

Find the probability that the sample mean of these 25 results, $Xˉ\bar{X}$ , is within $0.4$ ohms of $r$ .

[3]

Given that the mean of these 25 measurements is $120.4$ ohms, find a $95%95\%$ confidence interval for $r$ .

[3]

Markscheme

3.2 Finding Probabilities for Normal Distributions Questions

A Level
Maths
3.2 Finding Probabilities for Normal Distributions

80 exam-style questions on Edexcel A Level Maths 3.2 Finding Probabilities for Normal Distributions. Each one has a worked solution and a mark scheme showing where the marks go.

3.2 Finding Probabilities for Normal Distributions

Question bank

3.2 Finding Probabilities for Normal Distributions

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Question 1

An electronics engineer measures the resistance, $r$ ohms, of a specific component. The measured resistance, $X$ ohms, is normally distributed with mean $r$ ohms and standard deviation $0.8$ ohms.

Find the probability that $X$ is within $1.0$ ohm of $r$ .

[2]

The same component is measured 25 times and the results are recorded.

Find the probability that the sample mean of these 25 results, $Xˉ\bar{X}$ , is within $0.4$ ohms of $r$ .

[3]

Given that the mean of these 25 measurements is $120.4$ ohms, find a $95%95\%$ confidence interval for $r$ .

[3]

Markscheme

3.2 Finding Probabilities for Normal Distributions Questions

A Level
Maths
3.2 Finding Probabilities for Normal Distributions

80 exam-style questions on Edexcel A Level Maths 3.2 Finding Probabilities for Normal Distributions. Each one has a worked solution and a mark scheme showing where the marks go.