Final answer:
The probability density function for a U.S. male's height is normally distributed with mean 69 inches and standard deviation 2.8 inches, denoted as X~ N(69, 2.8). To find specific percentage or probabilities, z-score calculations utilizing the normal distribution are applied.
Step-by-step explanation:
The heights of males in the U.S. are approximately normally distributed with a mean (μ) of 69 inches and a standard deviation (σ) of 2.8 inches. If X represents the height of a randomly selected man in the U.S., the probability density function for X is given by the equation for a normal distribution, which we do not write out here in full but can generally be thought of as:
X ≃ N(69, 2.8)
To find the percentage of U.S. males taller than 6 feet (72 inches):
We would use a z-score calculation and look up the corresponding area to the right of the z-score on a standard normal distribution table or use a calculator with normal distribution functions. The area represents the percentage of males taller than 6 feet.
Inflection points of the probability density function:
The inflection points of a normal distribution curve occur at μ ± σ, which in this case would be at 69 ± 2.8 inches.
Percentage of Asian adult males taller than 72 inches:
Considering the average height of Asian adult males is 66 inches with a standard deviation of 2.5 inches, using a z-score calculation can yield the probability of an Asian adult male being taller than 72 inches, which is expected to be small.
For the mean height of Swedish males, using the given sample size and standard deviation, a 95 percent confidence interval can be constructed.
Estimating the mean height with a given confidence:
To estimate the mean height of students at a college to within 1 inch with 93 percent confidence, a sample size can be calculated using the z-score corresponding to the 93 percent confidence level and the known standard deviation of 2.5 inches.