A baby product company is considering to launch its new product, "baby cot" for newborn babies in two countries: United States and Thailand. The product will be sold to hospitals and used in the Obstetrics Department.

The length of newborn babies varies from country to country. For Thailand, the lengths can be well approximated by a Normal distribution having a mean 43.4 cm and standard deviation 3.5cm. For US, the length of new born babies can also be approximated by a Normal distribution with a slightly larger mean 45.7 cm and a standard deviation of 2.5cm.

Show your calculations and logic - and USE EXCEL FORMULAS to solve the following problems where applicable.

(a)The size of the company's cot is designed to be suitable for newborn babies having a length from 42 cm to 48 cm. The safety regulation of hospitals in both countries states clearly that newborns that do not fit these dimensions will not be allowed to use the cot. In which country does the company have a greater chance of its cot being accepted? Please show your calculations.

(b) The Company's product design department decides to adjust the size of cots. Because of some production constraints, the minimum newborn length that the re-designed cots can accommodate is still 42 cm. However, the company has some flexibility in accommodating larger newborn lengths. If the company aims to be able to accommodate at least 90% of newborn babies in the US what is the minimum upper limit of the cot size that will match the company's aim? Please give your answer as a whole number (without decimals). Briefly show your work.