The lifetimes of batteries used in a sensor are normally distributed. A supplier A A\,A sells batteries with a mean lifetime of 1200 hours and a standard deviation of 80 hours.
Find the probability of a battery from supplier A A\,A having a lifetime of less than 1100 hours.
In a shipment of 400 batteries from supplier AAA, find the expected number having a lifetime of less than 1100 hours.
Another supplier B B\,B sells batteries with a mean lifetime of 1250 hours, and it is known that 15% of these batteries have a lifetime of less than 1167 hours.
Find the standard deviation of the lifetimes of batteries from supplier BBB.
Both suppliers sell the batteries for the same price.
State which supplier you would recommend. 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.