Assume the Black-Scholes framework. You are given:

(i) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is identical to the continuously compounded (total) expected rate of return on the stock.

(ii) The expected 6-month stock price is 150.

(iii) The expected 6-month stock price, given that an at-the-money (when issued) 6-month European put option expires in-the-money, is 125.21.

Determine the 95% lognormal prediction interval for the 1-year stock price.