Final answer:
U.S. males taller than the average NBA player are fewer than average due to the normal distribution curve of heights. Very few individuals in the general population will surpass the NBA's mean height of 79 inches, as indicated by calculating z-scores.
Step-by-step explanation:
To estimate the number of U.S. males taller than the average NBA player, we first need to know that the average height of an NBA player is approximately 79 inches with a standard deviation of 3.89 inches. The heights of men in the U.S., and NBA players alike, follow an approximate normal distribution. Given this data, it is highly unlikely that the number of U.S. males taller than the average NBA player is greater than average. Using basic principles of a normal distribution curve, most of the population falls within three standard deviations of the mean. Thus, very few males are likely to exceed the height of an average NBA player. In short, the answer would be (b) Fewer than average.
For the heights of basketball players, calculating a z-score helps determine how far or how close a certain height is from the mean. For example, a player who is 77 inches tall would have a z-score of -0.5141, indicating they are below average height for an NBA player. Conversely, a player who is 85 inches tall would have a z-score of 1.5424, signifying they are significantly above average. Likewise, a z-score of 3.5 is extremely unlikely, as it would place the individual far beyond the range of typical player heights. When studying the height of other populations, such as Asian adult males or high school basketball players, it's evident that their average heights and standard deviations are much lower than those of NBA players. Hence, the proportion of these populations taller than the average NBA player would be even smaller.
In statistical studies, like measuring the height of college male students to estimate the mean height with a given confidence level, a sample size calculation is crucial. For instance, to estimate the mean height to within 1 inch with 93 percent confidence, a certain number of students must be sampled—the larger the desired confidence level and the smaller the margin of error, the larger the sample size required.