A data set with roughly a bell-shaped distribution has mean 45and standard deviation 12.Approximately what percentage of the observations lie between 33and 57?

Short Answer

Expert verified

The percentage of the observations lie between33and 57approximately are68%

Step by step solution

01

Given information

We are given that a data set with roughly a bell-shaped distribution has mean 45and standard deviation 12 .

02

Explanation

We will use empirical rule, to determine approximate values for the of observations between 33and 57.

We are given that μ=45andσ=12, where μis mean and σis standard deviation.

Also , the given interval 33,57will 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-kσ,μ+kσ=33,57k=1

By empirical rule , Pμ-σ<X<μ+σ0.68where Xis given interval.

So percentage is68%

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