In a controlled biochemical reaction, the concentration of enzyme E1, denoted by EEE mg/L, is measured. It is known that EEE follows a normal distribution with a mean of 45.0 and a standard deviation of 3.5.
(i) Find P(E<40.0)P(E < 40.0)P(E<40.0).
(ii) Find P(E>52.5)P(E > 52.5)P(E>52.5).
(iii) A quality control team defines 'optimal concentration' as being between 42.0 mg/L and 48.5 mg/L. Determine the proportion of enzyme samples that meet this criteria.
The system also monitors the gas pressure, SSS kPa, in the reaction vessel. The pressure SSS is normally distributed with mean μ\muμ and standard deviation σ\sigmaσ.
Environmental data shows that 20% of the pressure readings are less than 15.0 kPa, and 12% of the pressure readings are greater than 22.0 kPa.
Calculate the value of μ\muμ and the value of σ\sigmaσ for the gas pressure.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.