Answered: The amounts of nicotine in a certain…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.967 g and a standard deviation of 0.286 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 44 cigarettes with a mean nicotine amount of 0.881 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 44 cigarettes with a mean of 0.881 g or less.
P(M < 0.881 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 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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