Question

the table of random digits (table b) was produced by a random mechanism that gives each digit probability 0.1 of being a 0. (a) what proportion of the first 200 digits in the table are 0s? read the table from line 101 from the top left corner line by line. this proportion is an estimate, based on 200 repetitions, of the true probability, which we know is 0.1. give your answer to three decimal places.
proportion:
(b) the probability applet can imitate random digits. set the probability of heads in the applet to 0.1. check \show true probability\ to show this value on the graph. a head stands for a 0 in the random digit table and a tail stands for any other digit. simulate 200 digits (set the
umber of tosses\ to 200 and click on \toss\). make a note separately or on paper of the result of your 200 tosses.
assume another student used the probability applet as described to simulate the 200 digits. which of the statements is most likely to be true?

Explanation:

Step1: Understand the Problem

We need to find the proportion of 0s in the first 200 digits of Table B (random digits table). Each digit has a probability of 0.1 of being 0, but we need to count the actual number of 0s in 200 digits.

Step2: Analyze Table B (Assumed Process)

Typically, in a random digits table (like Table B), we would go through the first 200 digits (line by line, as per the problem: from line 101 top - left corner line by line) and count how many of them are 0. Let's assume we count the 0s. Suppose after counting, we find that out of 200 digits, there are, for example, 20 zeros (this is a common result due to the probability of 0.1, so \( \frac{20}{200}=0.100 \), but in practice, we need to actually count. However, since the problem is about estimation, and the true probability is 0.1, the proportion should be close to 0.1. But let's assume we do the counting:

Let's say we have a Table B (standard random digits table). Let's take line 101 (for example, in some standard Table B, line 101 might start with digits like: 19223 95034 05756 28713 96409 12531 42544 82853... but we need to go through 200 digits.

After carefully counting 200 digits (digit by digit), suppose we find that the number of 0s is \( n \). Then the proportion is \( \frac{n}{200} \).

For example, if in 200 digits, we count 20 zeros, then \( \frac{20}{200} = 0.100 \). If we count 18 zeros, it's \( \frac{18}{200}=0.090 \), if 22 zeros, \( \frac{22}{200} = 0.110 \). But since the problem says "Read the table from line 101...", and the true probability is 0.1, the proportion should be close to 0.1.

(Note: Since the actual Table B is needed, but in a typical scenario, the proportion of 0s in 200 random digits from Table B is close to 0.1. Let's assume we count and get, for example, 20 zeros. So \( \text{Proportion} = \frac{\text{Number of 0s}}{200} \).

Suppose after counting, the number of 0s is 20 (this is a common result as the expected value is \( 200\times0.1 = 20 \)). Then \( \frac{20}{200}=0.100 \).

Answer:

The proportion is close to 0.1 (for example, if we count 20 zeros, it's 0.100; the actual value depends on the table, but typically around 0.100).