Chapter 2: Q. 7 (page 139)

T2.7. If the heights of American men follow a Normal distribution, and $99.7 %$ have heights between $5^{'} 0^{''}$ and $7^{'} 0^{''}$ , what is your estimate of the standard deviation of the height of American men?
(a) $1^{''}$
(b) $3^{''}$
(c) $4^{''}$
(d) $6^{''}$
(e) $12^{''}$

Short Answer

Expert verified

The standard deviation of the height of American men is option (c) $4^{''}$ .

Step by step solution

Given information

The heights of American men follow a Normal distribution, and $99.7 %$ have heights between $5^{'} 0^{''}$ and $7^{'} 0^{''}$ .

Explanation

According to the $68 - 95 - 99.7$ rule, note that $99.7 %$ of the observation lies within three standard deviations of the mean $(μ \pm 3 σ)$

Then,
$μ - 3 σ = 5^{'}$ (1)

$μ + 3 σ = 7^{'}$ (2)

Subtract the equations (1) and (2), to obtain the value of standard deviation as, $\begin{aligned} \Rightarrow (μ + 3 σ) - (μ - 3 σ) = 7 - 5^{*} \end{aligned} \Rightarrow 6 σ = 2 \Rightarrow σ = \frac{2}{6} = 0.3333$

It is known that $12$ inches $(12^{*})$ constitutes 1 foot $(1^{'})$

Hence, the standard deviation is obtained as

$σ = 0.3333 \times 12 " = 4 "$

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T2.7. If the heights of American men follow a Normal distribution, and $99.7 %$ have heights between $5^{'} 0^{''}$ and $7^{'} 0^{''}$ , what is your estimate of the standard deviation of the height of American men?
(a) $1^{''}$
(b) $3^{''}$
(c) $4^{''}$
(d) $6^{''}$
(e) $12^{''}$

Short Answer

Step by step solution

Given information

Explanation

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T2.7. If the heights of American men follow a Normal distribution, and 99.7% have heights between 5'0'' and 7'0'', what is your estimate of the standard deviation of the height of American men?(a) 1''(b) 3''(c) 4''(d) 6''(e) 12''

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

T2.7. If the heights of American men follow a Normal distribution, and $99.7 %$ have heights between $5^{'} 0^{''}$ and $7^{'} 0^{''}$ , what is your estimate of the standard deviation of the height of American men?
(a) $1^{''}$
(b) $3^{''}$
(c) $4^{''}$
(d) $6^{''}$
(e) $12^{''}$