The Normal Distribution
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Question 204
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.[2]
Determine the probability that a randomly selected hole has a depth greater than 22 cm.
b.[3]
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)=0.90c.[4]
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.
The Normal Distribution Questions
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.