Question

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.883 g and a standard deviation of 0.313 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 32 cigarettes with a mean nicotine amount of 0.828 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 32 cigarettes with a mean of 0.828 g or less.
P(M < 0.828 g) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, is it valid to claim that the amoutn 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.

Answer 1

X : amounts of nicotine in a certain brand of cigarette

X ~ N( 0.883,0.313)

a sample size(n) is 32 .the sample mean will follow normal distribution with:-

mean = 0.883

the probability of randomly selecting 32 cigarettes with a mean of 0.828 g or less is:-

[ in any blank cell of excel type =NORMSDIST(-0.9946)]

No. The probability of obtaining this data is high enough to have been a chance occurrence.

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