Question

Assume the weights of painkiller pills are normally distributed with a mean of 500mg and a standard deviation of 75mg. If 81 pills are randomly selected, find the probability that they have a mean weight that is less than 475mg.

Answer 1

To find the probability that the mean weight of the 81 pills is less than 475mg, calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that the mean weight of the 81 pills is less than 475mg, we need to determine the z-score for this value and then use the standard normal distribution table.

1. Calculate the z-score: z = (475 - 500) / (75 / sqrt(81)) = -2.44
2. Look up the z-score in the standard normal distribution table to find the corresponding probability. The probability is approximately 0.0071.

Therefore, the probability that the mean weight of the 81 pills is less than 475mg is 0.0071, or 0.71%