Sample Problem

According to a survey, about 41% of U.S households own a basketball. You decide to ask 6 randomly selected households if they own basketballs. Use your graphing calculator to construct a histogram showing the binomial distribution for this situation. According to your histogram, what is the most likely number of households out of the six samples that own basketballs? What is the probability of getting this number (Enter your answer as a decimal rounded to the nearest thousandth)?

households at probability


After constructing a histogram, we can see that P(k = 2) = 6C2(0.41)2 (0.59)4≈0.306 is the greatest probability on the histogram.