Question

if you could please provide a step by step explanation I would really appreciate it

Discrete Random Variables Question 23. Let Y Bin(17,0.25) denote the binomially distributed random variable mea- suring the number of times an archer hits the bullseye. Calculate the probability that the archer scores exactly one or two arrows in the bullseye. Question 24. A dairy factory produces eleven buckets of milk and records the masses in kilograms. Compute to three decimal places the population mean and standard deviation of the bottle masses. 4.2,3.9, 4.0,4.1,3.8,3.7, 4.0,4.1, 4.3,4.0,3.9 Normal Distribution Il questions are to be solved using the provided cumulative distribution table for e standard normal variable Z ~ N(0, 1), or the equivalent normal variable func- tion on your calculator the Question 25. The height in metres of a growth of redwood trees is normally distributed, with nean 40 and variance 4. Determine the probability that a randomly chosen tree is between 1.5 metres and 3 metres taller than average. Question 26. Let X~ N(25, 4) be a random variable measuring the mass in kilograms of a population of turkeys. Suppose that M> 24 and the probability of a turkey having mass between 24kg and Mkg is 0.5997. Determine the value of M to two decimal places. [3 Financial Mathematics Question 27. A personal loan of $400.00 acquires simple interest at a rate of i per month. If the total amount to be repaid after one year is $654.00, then calculate the value of i to three decimal places. Bonus Question: Determine the accumulated value after 32 months on a principal of $1000 given a nominal annual interest rate of 5% compounded continuously. 12 Question 28. A car costing $20,000 is purchased on finance by Monopoly Man from the Seller of SUVs. An initial down-payment of S4000 is rnade, and the balance is to be anon tized by equal monthly installments over a period of four years. Given a repayment interest rate of 6% per annum compounded monthly: calculate how much of the first monthly payment is applied to the principal, and how much to interest.

Answer 1

23) Y w Bin(17, o. 25 one & 2 asiows in the oltays is 15 16