A medical researcher proposes to estimate the mean serum cholesterol level of a certain population of middle-aged men, based on a random sample of the population. He asks a statistician for advice.The ensuing discussion reveals that the researcher wants to estimate the population mean to within ±" style="box-sizing: border-box; -webkit-tap-highlight-color: rgba(0, 0, 0, 0); border: 0px; max-width: 100%; height: auto; display: inline; vertical-align: middle; line-height: inherit; max-height: 31.25rem; color: rgb(38, 38, 38); font-family: "Open Sans", sans-serif; font-size: 14px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">6 mg/dl or less, with 95% confidence. Thus, the standard error of the mean should be 3 mg/dl or less. Also, the researcher believes that the standard deviation of serum cholesterol in the population is probably about 40 mg/dl. How large a sample does the researcher need to take?