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2.4.12 Calculate probabilities from a Normal distribution (A-level only)

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Question 48

A manufacturing lab monitors the volume and composition of industrial coolant.

ai.

The volume, VVV ml, of a standard canister is modeled by a normal distribution with a mean of 450.5450.5450.5 and a standard deviation of 2.42.42.4.

Find the probability that a randomly selected canister contains exactly 450.5450.5450.5 ml of coolant.

[1]
aii.

Find the probability that a randomly selected canister contains more than 448.0448.0448.0 ml.

[2]
bi.

The mass, MMM grams, of the active chemical concentrate in a batch is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.

Given that P(M<215.5)=0.85P(M < 215.5) = 0.85P(M<215.5)=0.85, show that

215.5−μ=1.036σ 215.5 - \mu = 1.036\sigma 215.5−μ=1.036σ

where the constant is given to three decimal places. Fully justify your answer.

[2]
bii.

Given further that P(M<202.0)=0.08P(M < 202.0) = 0.08P(M<202.0)=0.08, find the values of μ\muμ and σ\sigmaσ.

[4]

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions

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