Question

Assume that the amount of time a person experiences cold virus symptoms are normally distributed with a mean of 7.5 days and a standard deviation of 1.5 days. what proportion of cold sufferers experience symptoms for more than 8 days? round your answer to four decimal places.

Answer 1

To find the proportion of cold sufferers who experience symptoms for more than 8 days, we calculate the z-score and find the area under the normal curve to the right of the z-score.

Step-by-step explanation:

To find the proportion of cold sufferers who experience symptoms for more than 8 days, we need to calculate the z-score using the formula:

z = (x - mean) / standard deviation

where x is the number of days, mean is 7.5 days, and standard deviation is 1.5 days.

Calculating the z-score:

z = (8 - 7.5) / 1.5 = 0.3333

Next, we determine the proportion of cold sufferers with symptoms lasting more than 8 days by calculating the area under the normal curve to the right of the z-score. We can use a standard normal table or a calculator to find this area. In this case, the area is 0.3707.

Therefore, approximately 0.3707 or 37.07% of cold sufferers experience symptoms for more than 8 days.