Chapter 3: Q. 3.131 (page 123)

The data set has $150$ observations and has mean $35$ and standard deviation $4$ . Approximately how many observations lie between $31$ and $39$ ?

Short Answer

Expert verified

Zero observations lies between $31$ and $39$ .

Step by step solution

Given information

We are given that the data has $150$ observations and

Mean $x = 35$

Standard deviation $s = 4$

We have to find number of observations between $31$ and $39$

Simplify

According to Chebyshev's Rule

For any quantitative data set and any real number $k$ greater than or equal to $1$ , at least $1 - \frac{1}{k^{2}}$ of the observations lie within $k$ standard deviations to either side of the mean, that is, between $x - k (s)$ and $x + k (s)$

Now, according to given data

$x - k (s) = 31 35 - k (4) = 31 k = 1 x + k (s) = 39 35 + k (4) = 39 k = 1$

Therefore, number of observations between $31$ and $39$ are $1 - \frac{1}{k^{2}} = 1 - 1 = 0$

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The data set has $150$ observations and has mean $35$ and standard deviation $4$ . Approximately how many observations lie between $31$ and $39$ ?

Short Answer

Step by step solution

Given information

Simplify

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The data set has 150observations and has mean 35and standard deviation 4. Approximately how many observations lie between 31and 39?

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

The data set has $150$ observations and has mean $35$ and standard deviation $4$ . Approximately how many observations lie between $31$ and $39$ ?