Final Answer:
The probability that 67 or 68 full-time workers are saving for retirement is approximately 0.1443.
Step-by-step explanation:
The given problem involves the approximation of the distribution of the number of full-time workers saving for retirement, denoted as x, with a normal distribution, n(64, 5.7), where the mean (μ) is 64 and the standard deviation (σ) is 5.7. In the context of this distribution, we are asked to find the probability that 67 or 68 full-time workers are saving for retirement.
To calculate this probability, we use the properties of the normal distribution. In a normal distribution, the area under the curve represents probabilities. The given mean (μ) is 64, and the standard deviation (σ) is 5.7. To find the probability that x is between 67 and 68, we calculate the z-scores for both values and then find the area under the curve between these z-scores.
After obtaining the z-scores, we refer to the standard normal distribution table or use a calculator to find the corresponding probabilities. The calculated probability for the range 67 to 68 full-time workers saving for retirement is approximately 0.1443.
This means that there is a 14.43% chance that the number of full-time workers saving for retirement falls within the specified range in the given normal distribution.