Mar \( 105: 13 \mathrm{pm} \) The height of adult women in the U.S are normally distributed with a mean of 64 inches and a standard deviation 3 inches. The probability that a randomly selected woman is taller than 67 inches is \( P(X>67)= \) normalcdf \( (67,1 E 99,64,3)=0.1587 \) The probability that a sample of 40 women has a mean height greater than 65 inches is \( P(X>65)= \) normalcdf( \( 65,1 E 99,64,3 / \) square root \( (40))=0.0041 \) \( \leftarrow \) Reply I Mark as Unread

Did you know that the concept of normal distribution was popularized in the 18th century by mathematician Carl Friedrich Gauss, who used it to describe the distribution of errors in measurements? This bell curve captures a plethora of natural phenomena, which is why it's a favorite in statistics. Just imagine how many fields—from psychology to agriculture—rely on this concept to make sense of their data! In the real world, understanding height distribution can play a crucial role in various industries. For instance, clothing manufacturers often use average height statistics to tailor designs and ensure a better fit for the majority of their customers. Similarly, healthcare professionals might depend on this data for assessing health trends and developing public health campaigns that target specific demographics. So, next time you pick out clothes, remember the science behind the sizes!