Final answer:
To determine the probability that a randomly selected teenager has between 1 and 2 teeth with fillings, we calculate the z-scores for 1 and 2 teeth with fillings, then subtract the cumulative probability of the lower z-score from the higher z-score using the standard normal distribution.
Step-by-step explanation:
To find the probability that a randomly selected teenager has between 1 and 2 teeth with fillings, given that teenagers have on average 2.8 teeth with fillings and a standard deviation of 0.7, we will use the normal distribution model. First, we need to convert the scores of 1 and 2 teeth with fillings into their respective z-scores using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For 1 tooth with fillings: z = (1 - 2.8) / 0.7 = -2.57
For 2 teeth with fillings: z = (2 - 2.8) / 0.7 = -1.14
Next, we look up these z-scores on the standard normal distribution table or use a calculator with normal distribution functions to find the probability associated with each z-score. The probability of a z-score between -2.57 and -1.14 represents the answer we're looking for.
Assuming we've found the probabilities P(z < -2.57) and P(z < -1.14) to be A and B respectively, the probability that a teenager has between 1 and 2 teeth with fillings is P(B) - P(A).