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 10 digits in the table are 0 s? Read the table from line 101 from the top left corner line by line. This proportion is an estimate, based on 10 repetitions, of the true probability, which we know is 0.1 . Give your answer to three 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 10 digits (set the "Number of Tosses" to 10 and click on "Toss"). Make a note separately or on paper of the result of your 10 tosses. Assume another student used the Probability applet as described to simulate the 10 digits. Which of the statements is most likely to be true? The student got one zero. The student got five zeros. If the student simulates, again he/she will get the same number of zeros. All of the other options are approximately equally likely.

To solve the problem, let's break it down into the two parts as specified. ### Part (a) 1. **Extract Known Conditions**: We need to find the proportion of zeros in the first 10 digits from line 101 of the random digit table. The true probability of getting a zero is 0.1. 2. **Read the Table**: Since I don't have access to the actual table, I will guide you on how to calculate the proportion once you have the digits. 3. **Calculate the Proportion**: - Count the number of zeros (let's denote this count as \( z \)) in the first 10 digits. - The proportion of zeros \( P \) can be calculated using the formula: \[ P = \frac{z}{10} \] - Once you have counted \( z \), substitute it into the formula to get the proportion. 4. **Final Answer**: Provide the proportion rounded to three decimal places. ### Part (b) 1. **Simulate with the Probability Applet**: Set the probability of heads (0) to 0.1 and simulate 10 digits. Record the results. 2. **Analyze the Statements**: - The probability of getting a zero in each toss is 0.1, and the probability of getting a non-zero is 0.9. - The expected number of zeros in 10 tosses can be calculated as: \[ E(z) = 10 \times 0.1 = 1 \] - The distribution of the number of zeros follows a binomial distribution \( B(n=10, p=0.1) \). 3. **Evaluate the Statements**: - **The student got one zero**: This is the expected outcome, and thus has a higher probability. - **The student got five zeros**: This is less likely since the expected number is only 1. - **If the student simulates again, he/she will get the same number of zeros**: This is not guaranteed; the number can vary with each simulation. - **All of the other options are approximately equally likely**: This is not true since the probabilities are not equal. ### Conclusion for Part (b) The most likely statement to be true is: - **The student got one zero.** This is because it aligns with the expected value based on the probability of getting a zero in each simulation.