The mass of precipitate, www grams, produced in a chemical reaction and the temperature, TTT ∘C{}^{\circ}\text{C}∘C, of the catalyst used are recorded for a random sample of 6 experimental runs, as shown in the table below.
| TTT (∘C{}^{\circ}\text{C}∘C) | 155 | 165 | 175 | 185 | 195 | 205 |
|---|---|---|---|---|---|---|
| www (grams) | 85.2 | 82.1 | 78.8 | 75.9 | 72.7 | 69.5 |
State, with a reason, which variable is the explanatory variable.
A linear model for www on TTT is
w=133.85−0.3138T w = 133.85 - 0.3138T w=133.85−0.3138TGive an interpretation of the gradient of this line.
Find the value of Tˉ\bar{T}Tˉ and the value of wˉ\bar{w}wˉ.
Show that the point (Tˉ,wˉ)(\bar{T}, \bar{w})(Tˉ,wˉ) lies approximately on the given line.
Use the given line to estimate the mass of precipitate for a reaction run with a catalyst temperature of 172 ∘C{}^{\circ}\text{C}∘C.
Comment, giving a reason, on the reliability of the estimate in part (e).
The mass of precipitate in this chemical process is assumed to be normally distributed with mean 76.5 grams and standard deviation 3.8 grams.
The middle 80% of precipitate masses lies between aaa and bbb.
Find the value of aaa and the value of bbb.
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.