After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95 percent confidence interval that goes from 0.36 to 0.54. True or False: This interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

The experiment is meant to measure potential customers that recognize a new product. So the potential customer can recognize the product or not, and in these cases, we say the variable (the thing we are studying) has a binomial distribution. The parameters are n (120) and p (54/120 = 0.45). As n is bigger than 30, we can't use the binomial distribution, we have to approximate it by using another one, in this case, the normal distribution. This is because not only n>30 but also because p is between 0.1 and 0.9 (0.1<p<0.9). So yes, in order to perfomr the interval of confidence, we have to assume that the number of people recognizing the product has a normal distribution. The parameters for the normal distribution will be mean (n*p = 54) and variance (n*p* (1-p) = 29.7), which makes a standard deviation of 5,44977 approximately. With those values we can build our confidence interval and seek the values of our variable.