Question

Records at a hospital show a certain surgical procedure takes an average of 162.8 minutes with a standard deviation of 4.9 minutes. If the data are approximately bell shaped, between what two values of 95 % of th data fall

Answer 1

Approximately 95% of the surgical procedure times fall between two standard deviations from the mean, which calculates to be between 153 and 172.6 minutes for the given data.

Step-by-step explanation:

The question is asking to find the range of values within which approximately 95% of the data fall for a normally distributed surgical procedure time, with a mean of 162.8 minutes and a standard deviation of 4.9 minutes. To solve this, we use the properties of the standard normal distribution. According to the empirical rule, also known as the 68-95-99.7 rule, approximately 95% of the data falls within two standard deviations from the mean. Therefore, we need to calculate the values two standard deviations away from the mean.

Step 1: Calculate the lower value by subtracting two standard deviations from the mean:

Lower Limit = Mean - 2(Standard Deviation) = 162.8 - 2(4.9) = 162.8 - 9.8 = 153

Step 2: Calculate the upper value by adding two standard deviations to the mean:

Upper Limit = Mean + 2(Standard Deviation) = 162.8 + 2(4.9) = 162.8 + 9.8 = 172.6

Therefore, approximately 95% of the surgical procedure times fall between 153 minutes and 172.6 minutes.