The Reserve Bank of Australia (RBA) slashed the official cash rate to a record low of 0.1 per cent in 2020 as an emergency response to the COVID-19 pandemic. An economist is interested in the average principal and interest repayment for a standard variable rate home loan entered into under the record low official rate. In mid-2020, 33 home loan customers with loans of the same characteristics were randomly sampled and asked how much they paid per month for their home loans. The descriptive statistics are shown in the table below. Descriptive Statistics for Home Loan Repayments in mid-2020 Mean Standard Error Standard Deviation Count 1271.96 26.85 154.24 33 Hint: For the first three questions you need to use the sample statistics (mean and standard deviation) to calculate a standardised value from a z or t distribution to be able to calculate this probability. We can assume that the average monthly repayment is normally distributed. 1. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is less than $1251.1? (3dp) 2. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is greater than $1309.23? (3dp) 3. (1 mark) What is the probability that a randomly selected home loan customer, that the monthly repayment is between there are between $1251.1 and $1309.23 ? (3dp)