Question

A survey found that womerts heights are normally distribused with mean 63.4 in and standard deviation 24 in. A branch of the military requires womeris heights to be between 58 in an a. Find the percentage of women mesting the heght requerement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall b. If this branch of the mhitary changes the hoight roquirements so that at women are eligble except the ahortest 1 N and the tallest 2 b. what are the new height requireinents? a. The percentage of women who meot the height requremert is (Round wis two decimal places as needed) Are many women being deried the opgortunity to join this beanch of the miltary because they are too short or too tall? A. Ves, bocause a targe percentage of women are not allowed to join this branch of the matary because of the hoight B. Yes, bocause tha percentage of women who meet the height requirement is farly large C. No, becaure the porcentige of women whe meet the height requiremert is taely small. D. No, becamze only a small percontage of women are not allowed to jon tus bronch of the miltary becaust of their height. b. For the now height requitemeris, this branch of the military requires womers heights fo be at least in and at aiost in (Round to ane decimal place as needed)

Answer 1

Normal distribution and its understanding are central to determining what percentage of a population falls within certain height requirements, as needed for military enlistment or engineering designs such as aircraft doorways.

Step-by-step explanation:

Understanding Normal Distribution in Relation to Women's Heights

The concept raised in the question relates to the normal distribution of heights among a population, which is a fundamental concept within statistics and probability. The normal distribution, often represented as a bell curve, is used to describe how the values of a variable are distributed. It implies that most observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. In this context, the heights of women are given as being normally distributed with a known mean and standard deviation.

Regarding the military requirements, the question pertains to finding the percentage of women who fall within a certain height range based on the given mean and standard deviation. Calculating this percentage involves using the cumulative distribution function for a normal distribution, which can be found using statistical tables or software that handle such calculations.

For part b, changing the height requirements involves finding the specific height measurements that exclude the shortest 1% and tallest 2% of the population. This also utilizes normal distribution properties, specifically the concept of z-scores, which represent the number of standard deviations an element is from the mean.

Finally, when designing doorways or other facilities where height is a limiting factor, the question becomes one of practicality and inclusion, taking into consideration the distribution of heights in the applicable population. Understanding normal distribution thus plays a crucial role in making data-driven decisions in engineering and resource allocation.