In Problems 5 and 6, determine the expected counts for each outcome.
[NOW WORK]

Verified step by step guidance

1. Identify the total number of trials or observations, which is given as \(n = 700\).
2. Note the probabilities for each outcome, which are \(p_1 = 0.15\), \(p_2 = 0.3\), \(p_3 = 0.35\), and \(p_4 = 0.20\).
3. Recall that the expected count for each outcome is calculated by multiplying the total number of trials by the probability of that outcome: \(\text{Expected count} = n \times p_i\).
4. Calculate the expected count for each outcome using the formula: \$700 \times 0.15\(, \)700 \times 0.3\(, \)700 \times 0.35\(, and \)700 \times 0.20$ respectively.
5. List the expected counts corresponding to each probability to complete the table.

Key Concepts

Expected Counts in Probability

Expected counts represent the average number of occurrences for each outcome in a sample, calculated by multiplying the total sample size by the probability of each outcome. This concept helps predict how often each category should appear under the assumed probability model.

Probability Distribution

A probability distribution assigns probabilities to all possible outcomes of a random experiment. Understanding the distribution is essential to calculate expected counts, as each probability value indicates the likelihood of a specific outcome.

Sample Size (n)

The sample size, denoted by n, is the total number of observations or trials in the experiment. It is crucial for determining expected counts because the expected count for each outcome is the product of n and the outcome's probability.