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Mathematics q. What is the minimum height ….?

Background>>> The true height of men is known as 173cm with a standard deviation of 6.5 cm. The proportion of men in the study are taller than 168cm is 78%. Q1. The builders want to make doors to suit at least 99% of men, which is the minimum height (to the nearest cm) must its doors? Any help much appreciated.

Let us assume that the height of men is a normal distribution. Then we can write this up as X = 173 + 6.5 * Z where Z is a standard distribution normal variable. Here we are in search of a height of x such that P (X <x)> = 0.99, in other words, so that the length of a random person is less than x with a probability of at least 99%. P (X <x) = P (173 + 6.5 * Z <x) = P (Z <[x - 173] / 6.5) = Phi ([x - 173] / 6.5) = 0, Phi 99 is cumulative distribution function of standard normal distribution. Therefore: (x – 173) / 6.5 = phi ^ (-1) (0.99) = 2.326, or in other words x = 173 + 6.5 * 2.326 = 188.12 cm to round, you get x = 189 cm. In conclusion, under the assumptions listed, the builders must design the doors of at least 189 cm, which at least 99% of all men can walk through without squatting.

Univariate Statistics in StatCrunch

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