Question

a sample of sand is taken at random from the shore of a lake. the table shows the estimated proportions of different materials present in the sample, with a margin of error of 0.07. based on these estimates and margin of error, which of the following is the most appropriate conclusion about the proportions of different materials present in the sand? a the proportion of organic matter will be lower than the proportion of basalt. b the proportion of garnet will be lower than the proportion of organic matter. c the proportion of garnet will be greater than 0. d the proportion of quartz will be greater than 0.61.

Explanation:

Step1: Analyze the given proportions

We are given the proportions of quartz = 0.68, basalt = 0.19, organic - matter = 0.12, and garnet = 0.01 with a margin of error of 0.07.

Step2: Check each option

• Option A: The proportion of organic matter (0.12) is not lower than the proportion of basalt (0.19). So, option A is incorrect.
• Option B: The proportion of garnet (0.01) is lower than the proportion of organic matter (0.12). So, option B is incorrect.
• Option C: The proportion of garnet is 0.01. With a margin of error of 0.07, the upper - bound of the proportion of garnet is \(0.01 + 0.07=0.08\) and the lower - bound is \(0.01 - 0.07=- 0.06\) (but proportion can't be negative, so we consider 0). Since the upper - bound is still less than 0.1, we can say that the proportion of garnet will be less than 0.1. This option is correct.
• Option D: The proportion of quartz is 0.68. With a margin of error of 0.07, the lower - bound of the proportion of quartz is \(0.68 - 0.07 = 0.61\) and the upper - bound is \(0.68+0.07 = 0.75\). So, we can't say for sure that the proportion of quartz will be greater than 0.7. This option is incorrect.

Answer:

C. The proportion of garnet will be less than 0.1.