Final answer:
Given the average outstanding payment of 230000 AED with a standard deviation of 45000 AED, and using the normal distribution, the Finance head is unlikely to cover 90% of the outstanding payments with 285000 AED, as 90% corresponds to 304025 AED which is greater than the available funds.
Step-by-step explanation:
The question is assessing whether the Finance head can pay 90% of the outstanding payments using 285000 AED, given the average outstanding payment is 230000 AED with a standard deviation of 45000 AED. To answer this, we would need to find what amount 90% of payments represent. As we don't have an exact distribution of the outstanding payments, we can't calculate the exact number of payments that can be covered, but we can make some assumptions based on the normal distribution.
If the outstanding payments are normally distributed, we can use the empirical rule, which would suggest that approximately 68% of the payments fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. If we assume a normal distribution, we can determine that 90% of the payments would likely fall below the mean plus 1.645 standard deviations (since 1.645 is the Z-score corresponding to the 90th percentile in a normal distribution).
Calculating this gives us 230000 AED + (1.645 * 45000 AED) = 304025 AED. This value represents the upper limit of what 90% of the branches will owe. Since this amount is greater than the 285000 AED the Finance head is willing to pay, it is unlikely they will be able to cover 90% of the outstanding payments.