The most recent public health statistics available indicate that 23.6% of American adults smoke cigarettes. Using the 68-95-99.7 Rule, describe the sampling distribution model for the proportion of smokers among a randomly selected group of 40 adults. Be sure to discuss your assumptions and conditions. Describe the sampling distribution. There is a 68% chance that between nothing% and nothing% are smokers, a 95% chance that between nothing% and nothing% are smokers, and a 99.7% chance that between nothing% and nothing% are smokers. (Round to one decimal place as needed.)

There is a 68% chance that between 17% and 30% are smokers.

There is a 95% chance that between 10% and 37% are smokers.

There is a 99.7% chance that between 4% and 44% are smokers.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of the sampling distribution of sample proportion is:

The standard deviation of the sampling distribution of sample proportion is:

Given:

n = 40

p = 0.236

Compute the mean and standard deviation of this sampling distribution of sample proportion as follows:

The Empirical Rule states that in a normal distribution with mean µ and standard deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be divided into three parts:

        That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.

        That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.

        That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

Compute the range of values that has a probability of 68% as follows:

Thus, there is a 68% chance that between 17% and 30% are smokers.

Compute the range of values that has a probability of 95% as follows:

Thus, there is a 95% chance that between 10% and 37% are smokers.

Compute the range of values that has a probability of 99.7% as follows:

Thus, there is a 99.7% chance that between 4% and 44% are smokers.

step-by-step explanation: