Question: Help me answer all the questions and explain all the steps Instructions: 1. Answer all questions. 2. Show all calculations and steps clearly. Separate marks

Help me answer all the questions and explain all the steps

Instructions: 1. Answer all questions. 2. Show all calculations and steps clearly. Separate marks will be awarded for correct answers and steps. 3. Display all non-integer numeric values to 4 decimal places. Question 1 (10 marks) The table below shows the cumulative frequency of the marks of 600 students in a mathematics contest. Marks |10 |20 30 |40 |50 |60 |70 80 |90 |100 |110 |120 | Cumulative | 10 145 220 295 480 | 540 575 Frequency (a) From the above table, find the five number summary of the distribution of marks. (8 marks) (b) A student with marks greater than or equal to 100 will be awarded a prize. If one student in chosen at random from the 600 students, find the probability that the student is a prize-winner. (2 marks) Question 2 (7 marks) A sporting brand was asked to sponsor a local boy in two golf tournaments. They claim the probability that he will win the first tournaments is 0.4. If he wins the first tournament, they estimate the probability that he will also win the second is 0.7. They guess that if he loses the first tournament, the probability that he will win the second is 0.3. (a) What is the probability that he wins both tournaments? (2 marks) (b) What is the probability that he wins the second tournament? (3 marks) (c) Use the results of part (a) and (b) to show that the two tournaments are not independent. (2 marks) Question 3 (13 marks) Assume the number of calories in a McDonald's Egg McMuffin is a normally distributed random variable with a population mean of 266 calories and a population standard deviation of 14 calories. (a) What is the probability that a particular serving contains between 280 and 301 calories? (6 marks) (b) According to the Dietary Guidelines for Americans, men typically need between 2000 and 3000 calories a day. If an adult male only eats 8 McDonald's Egg McMuffin in one day, how likely that the total calories attainment will be less than the minimum requirement? (4 marks) (c) In part (b), do you rely on the Central Limit Theorem? Explain your

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