Question

The Finesse Door Company manufactures doors for recreational vehicles. It has two
conflicting objectives. It wants to build doors as small as possible to save on material costs,
but to preserve its reputation with the public, it feels obliged to manufacture doors that are
tall enough for 95% of the adult population in India to pass through without stopping. To
determine the height at which to manufacture doors, Finesse is willing to assume that the
height of adults in India is normally distributed with mean 73 inches and standard deviation 6
inches. How tall should Finesse’s doors be?​

Answer 1

Beklager☹️

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India has been a secular federal republic since 1950, governed in a democratic parliamentary system. It is a pluralistic, multilingual and multi-ethnic society. India's population grew from 361 million in 1951 to 1,211 million in 2011.[49] During the same time, its nominal per capita income increased from US$64 annually to US$1,498, and its literacy rate from 16.6% to 74%. From being a comparatively destitute country in 1951,[50] India has become a fast-growing major economy, a hub for information technology services, with an expanding middle class.[51] It has a space programme which includes several planned or completed extraterrestrial missions. Indian movies, music, and spiritual teachings play an increasing role in global culture.[52] India has substantially reduced its rate of poverty, though at the cost of increasing economic inequality.[53] India is a nuclear-weapon state, which ranks high in military expenditure. It has disputes over Kashmir with its neighbours, Pakistan and China, unresolved since the mid-20th century.[54] Among the socio-economic challenges India faces are gender inequality, child malnutrition,[55] and rising levels of air pollution.[56] India's land is megadiverse, with four biodiversity hotspots.[57] Its forest cover comprises 21.4% of its area.[58] India's wildlife, which has traditionally been viewed with tolerance in India's culture,[59] is supported among these forests, and elsewhere, in protected habitats.

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Answer 2

Concept:

Percentile Value = μ + zб

where:

μ - Mean

μ - Meanz - z-score from z table that corresponds to percentile value

б - Standard deviation

Find:

We find the height of 95th percentile door

Given:

We given that

Mean = 73 inches

standard deviation = 6

Explantion:

We given

Mean = 73 inches

standard deviation = 6

To answer this, we must find the z score that is closest to the value 0.95 in the z table. This value turns out to be 1.64

We can then plug this value into the percentile formula:

Percentile Value = μ + zб

95th percentile = 73 + (1.64) 6

95th percentile = 73 + 9.84

95th percentile = 82.84

An otter at the 95th percentile height about 82.82 inches.

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