Interactive practice questions
The mean of a set of scores is $77$77 and
the standard deviation is $29$29. Find the value of:
$\text{Mean }-\text{Standard Deviation}$Mean −Standard Deviation
$\text{Mean }+2\times\text{Standard Deviation}$Mean +2×Standard Deviation
$\text{Mean }-\frac{\left(2\times\text{Standard Deviation}\right)}{3}$Mean −(2×Standard Deviation)3
$\text{Mean }+\frac{\left(4\times\text{Standard Deviation}\right)}{5}$Mean +(4×Standard Deviation)5
$\text{Mean }+3\times\text{Standard Deviation}$Mean +3×Standard Deviation
$\text{Mean }-2\times\text{Standard Deviation}$Mean −2×Standard Deviation
The following figure shows the approximate percentage of scores lying within various standard deviations from the mean of a normal distribution. The heights of $600$600 boys are found to approximately follow such a distribution, with a mean height of $145$145 cm and a standard deviation of $20$20 cm. Find the number of boys with heights between:
Complete the following statements for a normal distribution using the empirical rule.
In a normal distribution, what percentage of scores lie between the mean and $1$1 standard deviation above the mean? Use the empirical rule to find your answer.