Final answer:
To find the probability that the proportion of individuals in the sample who hold multiple jobs is between 0.055 and 0.10, we can use the normal distribution and calculate the z-scores for the lower and upper boundaries of the desired proportion range. By finding the corresponding population proportions using the z-scores, we can calculate the probability by subtracting the upper probability from the lower probability.
Step-by-step explanation:
The probability of the proportion of individuals in the sample of 255 who hold multiple jobs being between 0.055 and 0.10 can be found using the normal distribution. This involves calculating the z-scores for the lower and upper boundaries and then using a z-table or calculator to find the corresponding probabilities. The formula for calculating the z-score is:
z = (x - p) / sqrt(p*(1-p)/n)
where x is the sample proportion, p is the population proportion, and n is the sample size.
Firstly, we calculate the z-score for the lower boundary 0.055:
z = (0.055 - p) / sqrt(p*(1-p)/255)
After rearranging the formula, we can solve for p:
p = (0.055 * sqrt(p*(1-p)/255)) + 0.055
We repeat the same steps for the upper boundary 0.10:
p = (0.10 * sqrt(p*(1-p)/255)) + 0.10
By solving these equations, we can find the corresponding population proportion p for each boundary. The probability can then be calculated by subtracting the two probabilities:
probability = p_upper - p_lower