The tensile strengths of alloy cables produced by industrial extrusion machines are normally distributed. Machine XXX produces cables with a mean tensile strength of 450 MPa and a standard deviation of 24 MPa.
Find the probability that a cable from Machine XXX has a tensile strength of less than 414 MPa.
In a production batch of 600 cables from Machine XXX, determine the expected number of cables having a tensile strength of less than 414 MPa.
Another machine, Machine YYY, produces cables with a mean tensile strength of 465 MPa. It is known that 12%12\%12% of these cables have a tensile strength of less than 435.6 MPa.
Calculate the standard deviation of the tensile strengths of cables from Machine YYY.
Both machines operate at the same utility cost per cable.
State which machine you would recommend for procurement. Give reasons for your answer.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.