I want to know if the simple random sample con tino is met. And if the sigma is unknown. And if the sample size condition is met

Chapters 8 Assignment 1. A random sample of 100 households in Whatcom County yielded an average household income of $86,000, with a sample standard deviation of $3,600. Assume the distribution of household income is Normal. a. Use this information to compute a 95% confidence interval for the population mean household income in Whatcom County. Please clearly show that you checked to make sure the data meet all necessary conditions for inference