Discrete Probability Distributions Lefties Suppose a friend of yours told you that 10% of people in the population are left-handed. You randomly select 15 people from and count the number of lefties...

Discrete Probability Distributions Lefties Suppose a friend of yours told you that 10% of people in the population are left-handed. You randomly select 15 people from and count the number of lefties in the sample, denoted X. Answer the following questions assuming people are either left or right handed but not both. Find out the probability distribution of X and present the probability distribution in the form of a table using 5 decimal points in your answers. (You have to use Excel to calculate the probabilities, as the binomial table only gives the probabilities correct to 3 d.p.) (2 marks) How many lefties would you expect the sample of 15 contains using the formula of expected value of discrete random variable the binomial formula for expected value (Show working.) (2 marks) Explain what expectation in statistics means in the context of the Lefties example. (2 marks) What is the probability of getting 5 or more lefties in the sample of 15? (Show working.) (2 marks) If the sample contains 5 lefties, would you suspect your friend might be wrong? Discuss fully. (type I error) (2 marks) Submit a single document in pdf format