Academic presentation for college course (paper and pencil design)

normal curveMrs. Aldous, Mr. Beetz & Mr. ThauvetteDP SL Mathematics1Normal DistributionYou should be able toDescribe the properties of a normal distribution with mean and standard deviation

Calculate normal probabilities

Find the corresponding standardized value (z score) given a probability

You should be able toUse the relation to standardize data

or to find missing parameters and/or when given probabilities

Use the GDC to find normal probabilities or standardized values.

What is normal distribution?Mean, median, and mode

The Normal Distribution: A probability distribution where the mean, median, and mode are at the centre of the spread.Are these normally distributed?heights and mass of peopleIQ scoresScores in an examinationlifetime of a batteryNotation for normal distributionThe distribution of Xis normally distributedwith a mean ofand a variance of .

Note the variance is often the written as the standard deviation squared.Write down the mean and standard deviation of each of the following normal distributions.

Heights of UK AdultsWrite probability distributions to describe the heights of men and women.Does it matter if you use feet and inches, only inches, or centimeters?The distributions are the same regardless of which units you choose to use. This discussion should allow students to see how all normal distributions share the same shape. This helps justify the use of the standard normal distribution.7Standardizing dataFor the normal distribution we can standardize the data. All standardized data has a mean of 0, and a variance (and standard deviation) of 1.01-1

Each 1 unit away from the mean is a standard deviation.The standardized values are called z numbers.The area under this curve is 1.Using a GDC for standardized dataIf you are able to use a GDC for finding normal values then this is an easy and quick method.1. Draw a sketch.2. Use DISTR > normalcdf(.3. Enter lower and upper bounds. Use -1E99 or 1E99 for .4. Leave the mean as 1 and the standard deviation as 0.What is the probability that z is less than (or equal to) 1?

P(z-1.21)

4. P (z2.0.1940.2610.998

0.1040.135

Probability Tarsia Puzzle

You need the information sheet and a set of 24 triangles.

ExampleA factory makes calculators. Over a long period, 2% of them are found to be faulty. A random sample of 100 calculators is tested.(a) Write down the expected number of faulty calculators in the sample.

(b) Find the probability that three calculators are faulty.

Example continued(b) Find the probability that three calculators are faulty.

Example continued(c) Find the probability that more than three calculators are faulty.

Example continuedUsing the GDC (c) Find the probability that more than three calculators are faulty.

How do I approach this question?What are the key area from the syllabus?(a)

(b) Find the complement of

You should knowA binomial experiment is one in which there are n independent trials. For each trial, there are only two outcomes: a success and a failure. For example, tossing a coin 10 times, consider heads success and tails failure

We write to refer to a random variable of a binomial experiment with n independent trials and probability of a success, p

You should knowThe probability of r successes in n trials is given by

where 1 p is the probability of a failure

The mean of a binomial distribution is given by

The variance of a binomial distribution is given by

Be preparedRemember, when calculating a binomial probability, dont forget that, in order for there to be exactly r successes, there must also be n r failures. The (1 p)n r factor must not be omitted.When finding cumulative probabilities less than a number dont forget to include P(X = 0) in your calculation, that is,