IBDP Mathematics Applications & Interpretations SL Chapter 7 Notes

Quantifying uncertainty: probability, binomial and normal distributions

STUDY NOTES FOR MATHEMATICS – CHAPTER 7 – Quantifying uncertainty: probability, binomial and normal distributions

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Probability concerns numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where 0 indicates impossibility of the event and 1 indicates certainty. In this chapter we learn about trials, outcomes, sample space and events, the probability of an event, complementary events, combined events, mutually exclusive events, conditional probability, probabilities of independent events, venn and tree diagrams and lastly table of outcomes.

Furthermore, this chapter deals with the various types of distribution, such as binomial, poisson distribution and how we can use technology to solve them.

In this chapter, we consider the variables with symmetrical, bell-shaped distribution curves. We call this a normal distribution. This happens to be the most important distribution in statistics. The normal distribution arises in nature when many different factors affect the value of the variable. Some examples of quantities that may be normally distributed or approximately normally distributed are: the heights of 15 year old girls, the volumes of liquid in soft drink cans, the length of adult sharks, etc. The exact location and shape of the curve is determined by the mean which measures the centre of the distribution, and the standard deviation which measures the speed of the distribution. We then later calculate probabilities using normal distribution.