The range of a set of measurements is the difference between the largest and the smallest values. The empirical rule suggests that the standard deviation of a set of measurements may be roughly approximated by one-fourth of the range (that is, range/4 ).

The acidity of soils is measured by a quantity called the pH, which may range from 0 (high acidity) to 14 (high alkalinity). A soil scientist wants to estimate the average pH for a large field by randomly selecting n core samples and measuring the pH in each sample. Although the population standard deviation of pH measurements is not known, past experience indicates that most similar soils have a pH value between 5.4 and 8.8 .

Suppose the scientist would like the sample mean to be within 0.19 of the true mean with probability 0.90 . What is the minimum number of core samples the scientist should take? (Round your answer up to the nearest whole number.)