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

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Question 44

The lengths, LLL mm, of precision-machined alloy rods are modeled by a normal distribution with mean 24.0 mm24.0\text{ mm}24.0 mm and standard deviation 0.5 mm0.5\text{ mm}0.5 mm.

a.

Find P(L>25.1)P(L > 25.1)P(L>25.1).

[3]
b.

Find, to one decimal place, the value of kkk such that P(L<k)=3P(L>k)P(L < k) = 3 P(L > k)P(L<k)=3P(L>k).

[3]
c.

Write down the name given to the value of kkk.

[1]
d.

For a different grade of rod, the lengths are normally distributed with mean 30.0 mm30.0\text{ mm}30.0 mm.

Given that the 90th percentile for this grade of rod is 31.922 mm31.922\text{ mm}31.922 mm,

find the standard deviation of the length of this grade of rod.

[3]

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

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