please help this probability and statistics questions with steps, thanksss

(10 marks) Many medical professionals believe that smoking increases the risk of heart disease and cancer. A medical researcher would like to conduct a survey to determine the monthly consumption of cigarettes by a typical consumer (i.e-, to estimate the average monthly consumption of smokers)- Her research budget is $2,000 and the cost of collecting an observation is $10. Her target is to nd a 90% confidence interval estimate with a range of 3 cigarettes. If the population standard deviation is 12 cigarettes, is her budget sufficient for conducting such a survey to achieve her target? Explain