1. The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.952 g and a standard deviation of 0.316 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 45 cigarettes with a mean nicotine amount of 0.895 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 45 cigarettes with a mean of 0.895 g or less. P(M < 0.895 g) = Enter your answer as a number accurate to 4 decimal places. Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

2. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.2 years, and standard deviation of 1.3 years. If 24 items are picked at random, 7% of the time their mean life will be less than how many years? Give your answer to one decimal place.