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2.4.6 Probabilities using the normal distribution (A-level only)

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Question 69

The random variable XXX is normally distributed with mean μ\muμ and variance 252525. Given that P(μ−3k<X<μ+3k)=0.7P(\mu - 3k < X < \mu + 3k) = 0.7P(μ−3k<X<μ+3k)=0.7:

a.

find the value of kkk.

[3]
b.

The random variable YYY is normally distributed with mean μ\muμ and standard deviation σ\sigmaσ. Given that 3μ=4σ23\mu = 4\sigma^23μ=4σ2 and P(Y>54μ)=0.0228P\left(Y > \frac{5}{4}\mu\right) = 0.0228P(Y>45​μ)=0.0228: find the value of μ\muμ and the value of σ\sigmaσ.

[5]

2.4.6 Probabilities using the normal distribution (A-level only) Questions

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