Chapter 3: Q. 11 (page 151)

A data set of size $152$ with roughly a bell-shaped distribution has mean $25$ and standard deviation $4$ $4$ .
Approximately how many observations lie between $17$ and $33$ ?

Short Answer

Expert verified

The observations that lie between $17$ and $33$ approximately are $144$

Step by step solution

Given information

We are given that a data set of size $152$ with roughly a bell-shaped distribution has mean $25$ and standard deviation $4$ .

Explanation

We will use empirical rule, to determine approximate values for the of observations between $17$ and $33$ .

We are given that $μ = 25$ and $σ = 4$ , where $μ$ is mean and $σ$ is standard deviation.

Also , the given interval $(17, 33)$ will be formed by adding and subtracting standard deviations from the mean .We will check for different values of $k$ .

So using the value of mean and standard deviation , we get , $(μ - k σ, μ + k σ) = (17, 33)$ $\Rightarrow k = 2$

By empirical rule , $P (μ - k σ < X < μ + k σ) \approx 0.95$ where $X$ is given interval.

So percentage is $95 %$

To find observations, we will use $95 %$ of $152$ is $144.4$

So approximate value is $144$

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A data set of size $152$ with roughly a bell-shaped distribution has mean $25$ and standard deviation $4$ $4$ .
Approximately how many observations lie between $17$ and $33$ ?

Short Answer

Step by step solution

Given information

Explanation

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A data set of size 152with roughly a bell-shaped distribution has mean 25and standard deviation44.Approximately how many observations lie between17 and 33 ?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

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A data set of size $152$ with roughly a bell-shaped distribution has mean $25$ and standard deviation $4$ $4$ .
Approximately how many observations lie between $17$ and $33$ ?