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

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Question 70

An agricultural company monitors the weight of crop yields.

ai.

The weight, XXX kg, of a sack of potatoes is modeled by a normal distribution with a mean of 25.4 and a standard deviation of 0.8.

Find the probability that a randomly selected sack of potatoes weighs exactly 25.4 kg.

[1]
aii.

Find the probability that a randomly selected sack of potatoes weighs more than 24.5 kg.

[2]
bi.

The weight, YYY kg, of a sack of onions is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.

Given that P(Y<12.8)=0.9P(Y < 12.8) = 0.9P(Y<12.8)=0.9, show that

12.8−μ=1.282σ 12.8 - \mu = 1.282\sigma 12.8−μ=1.282σ

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

[2]
bii.

Given further that P(Y<10.2)=0.05P(Y < 10.2) = 0.05P(Y<10.2)=0.05, find the values of μ\muμ and σ\sigmaσ.

[4]

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

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