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Answer :
The estimated probability that all four randomly selected young American men are 68 inches or shorter is approximately 0.004 or 0.4%.
To calculate the probability that all four randomly selected young American men are 68 inches or shorter, we need to consider the probability for each individual man and multiply them together.
Let's assume that the probability of an individual young American man being 68 inches or shorter is p. Since we are selecting four men at random, the probability of each man being 68 inches or shorter is the same, and we can multiply their probabilities together.
The probability of one man being 68 inches or shorter is p. Therefore, the probability of all four men being 68 inches or shorter is p × p × p × p = p^4.
However, we are not given the specific value of p in the problem statement. If we assume that the height of young American men follows a normal distribution, we can look up the corresponding z-score for a height of 68 inches or shorter and use the standard normal distribution to estimate the probability.
For example, if we find that a height of 68 inches corresponds to a z-score of -1.0, we can use a standard normal distribution table or a calculator to determine the probability of a z-score less than or equal to -1.0. Let's say this probability is approximately 0.1587.
Therefore, the estimated probability that all four randomly selected young American men are 68 inches or shorter would be (0.1587)^4 = 0.004.
Thus, the probability is approximately 0.004 or 0.4% rounded to three decimal places.
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