Introduction to Probability and Statistics

QUESTION E a} A company makes electronic motors. The probability that an electric motor is defective is 0.1111. What is the probability that a sample of 30".] electric motors will contain exactly 5 defective motors'il {4 marks] b} Past record show that the times. in seconds, taken to run 100 m by children at a school can be modeled by a normal distribution with a mean of 15.12 and a standard deviation of 1.5:]. i) A child from the school is selected at random. Find the probability that this child ans 10o m in less than '15 seconds. {3 marks) ii] [in sports day the school awards medals to the fastest 30% cf the children in the 100 m race. Estimate the slowest time taken to mn mu m for which a child will be awarded a medal. [3 marks)