Final answer:
The question tells us that the sample proportion of teenagers who approve of legal gambling or betting follows a normal distribution with a mean of 0.5 and a standard deviation of 0.022. The probability that fewer than 54.4% of teenagers say yes is low.
Step-by-step explanation:
To solve this problem, we can use the concept of the standard normal distribution. The question tells us that the sample proportion of teenagers who approve of legal gambling or betting follows a normal distribution with a mean of 0.5 and a standard deviation of 0.022.
We want to find the probability that fewer than 54.4% of teenagers say yes.
We can convert this into a standard normal distribution by subtracting the mean and dividing by the standard deviation. The standardized value for 54.4% is (54.4% - 50%)/0.022 = 4.4/0.022 = 200.
Using the 68-95-99.7 rule, we know that 95% of the values fall within 2 standard deviations of the mean.
Since we are looking for values that are less than 54.4%, which is more than 2 standard deviations above the mean, the probability would be close to 0. Therefore, the probability that fewer than 54.4% say yes is very low.