Answer
a) 0.001 b)0.271 c)$n\cdot p$ is less than 5, hence the normal approximation would result in large errors d)5 e)2.1 f) could easily occur
Work Step by Step
a) By using the multiplication rule: $P(3 \ left \ handed \ people)=P(left \ handed)^3=0.1^3=0.001.$ b) Using the complement and multiplication rule: $P(at \ least \ 1 \ left \ handed \ people)=1-P(no \ left \ handed)^3=1-0.9^3=0.271.$ c)$n\cdot p$ is less than 5, hence the normal approximation would result in large errors d) The probability of someone being left-handed is 0.1, hence the mean is: $(sample \ size) \cdot probability= 50\cdot 0.1=5.$ e) Standard deviation:2.1. f) 8 is within 2 standard deviations from the mean, hence it could easily occur.
