At Riverbank State park the maximum allowable standard for swimming in the lake are 235 colonies of E. coli per 100 mlof water. In order to measure this, 10 different measurements of E. coli are taken each day at different locations in the lake near the beach. On a given day, the 10 measurements were 118, 175, 190, 206, 207, 208, 249, 256, 260, and 289.

Assuming the underlying distribution of E. coli counts is normal, construct a 95% confidence interval for the true mean number of colonies of E. coli per 100 ml of water.

answer is upper: 251.30

lower bound: 180.30

please explain in detail step by step