Finding Expected Frequencies
In Exercises 3–6, find the expected frequency for the values of n and pᵢ.


n=500, pᵢ=0.9

Verified step by step guidance

1. Step 1: Recall the formula for expected frequency, which is given by E = n × pᵢ, where E is the expected frequency, n is the total number of trials, and pᵢ is the probability of success for a specific category.
2. Step 2: Identify the values provided in the problem. Here, n = 500 (total number of trials) and pᵢ = 0.9 (probability of success for the category).
3. Step 3: Substitute the given values into the formula. This means replacing n with 500 and pᵢ with 0.9 in the equation E = n × pᵢ.
4. Step 4: Perform the multiplication to calculate the expected frequency. Specifically, multiply 500 by 0.9 to find the value of E.
5. Step 5: Interpret the result. The expected frequency represents the number of occurrences you would expect in the category with probability pᵢ = 0.9 out of 500 trials.

Key Concepts

Expected Frequency

Expected frequency refers to the anticipated number of occurrences of a particular outcome in a statistical experiment, calculated by multiplying the total number of trials (n) by the probability of the outcome (pᵢ). In this case, it helps in determining how many times we expect a specific event to happen based on the given probability.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of this question, pᵢ represents the probability of a specific outcome occurring in a sample of size n, which is crucial for calculating expected frequencies.

Sample Size (n)

Sample size (n) refers to the total number of observations or trials in a statistical study. A larger sample size generally provides more reliable estimates of expected frequencies, as it reduces the impact of random variation and allows for better generalization of results to the population.