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

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

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Question 10

The random variable D D\,D represents the depth, in cm, of a hole created by an automated drill. It is known that D D\,D follows a normal distribution with mean 18 and standard deviation 5.

a.

Determine the probability that a randomly selected hole has a depth greater than 22 cm.

[2]
b.

Find the value of c c\,c such that

P(18−c<D<18+c)=0.90 P(18 - c < D < 18 + c) = 0.90 P(18−c<D<18+c)=0.90
[3]
c.

A single observation d d\,d of D D\,D is to be taken. A rectangle is constructed on a coordinate grid with vertices at the points (0,0)(0, 0)(0,0), (d,0)(d, 0)(d,0), (d,d−3)(d, d - 3)(d,d−3), and (0,d−3)(0, d - 3)(0,d−3).

Find the probability that the area of this rectangle is more than 180 cm2^22.

Coordinate grid showing a rectangle with vertices (0, 0), (d, 0), (d, d - 3), and (0, d - 3).

[4]
Markscheme

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

  1. A Level
  2. /Maths
  3. /2.4.6 Probabilities using the normal distribution (A-level only)

147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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