The tensile strength of carbon fiber filaments produced by a high-precision spinning machine is modeled by a normal distribution with a mean of 4500 MPa. Internal quality control reports indicate that only 0.5% of the filaments produced have a tensile strength exceeding 4560 MPa.
Write down the percentage of filaments with tensile strengths between 4440 MPa and 4560 MPa.
Calculate the standard deviation of the tensile strengths for these filaments.
A technician performs a routine check by selecting a filament at random and measuring its strength. If the measured strength deviates from the mean by more than 30 MPa, it is classified as 'irregular'. If an irregular filament is found, a second filament is selected at random and tested. The machine is recalibrated only if both tested filaments are found to be irregular.
Determine the probability that the machine is recalibrated following such a check.
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.