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yanalaym [24]
3 years ago
5

In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviatio

n of 3 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.
Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer:

Two intervals are 63 and 75

Step-by-step explanation:

Given:

Mean of students (μ) = 69 inches

Standard deviation (σ) = 3 inches μ

Find:

Interval of heights (95%) using empirical rule

Computation:

Interval of heights (95%) using empirical rule:

⇒ μ – 2σ = 69 - 2(3)

⇒ μ – 2σ = 69 - 6

⇒ μ – 2σ = 63

⇒ μ + 2σ = 69 + 2 (3)

⇒ μ + 2σ = 69 + 6

⇒ μ + 2σ =  75

Two intervals are 63 and 75

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Given that:

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Therefore;

The standard error is determined as:

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\sigma_{\bar x} = 1.414

d) When the population size N= 500

n/N = 50/500 = 0.1 > 0.05

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Therefore;

The standard error is determined as:

\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }

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