Jazzy Maths
|[pic] |[pic] |[pic] |
|….greater than 4….. | X>4 | 1 ̶ P(X≤4) |
|….no more than 5…. | X≤5 | |
|….at least 8…. | | |
|….fewer than 11…. | | |
|….at most 3…. | | |
9b) Explain in words what is meant by the mean , E(X), the standard deviation σ and the variance Var(X) in statistical problems. State the formulae for E(X) and Var(X) in the binomial distribution
9c) Two cricketers Alistair Rook and Kevin Pietersing both have mean scores of 45 runs respectively in a season. Their standard deviations are 15 and 30 runs respectively. Who is most likely to achieve a century (a hundred runs)?
10. Of the articles from a certain production line, 10% are defective. If a sample of 25 articles is taken, find the expected number of defective articles and the standard deviation. Explain what these mean in words in the context of the question.
11. In a group of people, the expected number who wears glasses is 2 and the variance is 1.6. Find the probability that:
(a) a person chosen at random from the group wears glasses.
(b) 6 people in the group wear glasses
12. If the random variable X is such that X ~ B (10, p ) where p < ½ and Var(X) = 17/8, find
(a) p (b) E(X) (c) P(X = 2)
13. A class contains 30 children; 18 girls and 12 boys. Four complementary theatre tickets are distributed at random. What is the probability that:
(a) all 4 tickets are given to girls (b) 2 tickets go to boys and 2 to girls
Challenge
A cube ABCDEFGH has the square ABCD as its base with EGFH above ABCD respectively. What is the cosine of the angle CAG?
Preparation
Implicit Differentiation
Some algebraic expressions cannot be easily rearranged to isolate the variable y to find [pic] and so we differentiate implicitly. Read about how and when this is used new textbook pages 39-41 old textbook pages 35-37
Drill Answers*
* any errors/typos in answers please email the correct answer to v.moore@bhasvic.ac.uk
Part A (a) [pic] (b) [pic] (c) [pic]
Part B (a), (b) change of sign (c) f(x) is not continuous on the interval. Have a look at it in your graphics or on Autograph
Part C (a) 4 , 12 (b) [pic]
Part D check graphs in the C3 text book, on graphics or Autograph
The range of a function is the domain of its inverse
(a) domain x εR: -1 ≤x ≤1, range yεR: -π/2≤ y ≤ π/2
(b) domain x εR: -1≤x≤1, range yεR: 0 ≤ y ≤ π
(c) domain xεR, range yεR: -π/2< y ................
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