The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.951 g and a standard deviation of 0.307 g. The company that produces these cigarettes claims that it...

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.951 g and a standard deviation of 0.307 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 38 cigarettes with a mean nicotine amount of 0.876 g.


Assuming that the given mean and standard deviation
have NOT changed, find the probability of randomly selecting 38 cigarettes with a mean of 0.876 g
or less.

Based on the result above, is it valid to claim that the probability of this data is unlikely to have occurred by chance alone?