Question

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data greater than 6.9.

Answer 1

Step 1:

Give data

`\begin{gathered} mean\text{ }\mu\text{ = 5.1} \\ standard\text{ }\sigma\text{ = 0.9} \\ \text{x = 6.9} \end{gathered}`

Step 2:

Find the z-score

`\begin{gathered} \text{z = }\frac{x\text{ - }\mu}{\sigma} \\ \text{z = }\frac{6.9\text{ - 5.1}}{0.9} \\ \text{z = 2} \end{gathered}`

Step 3:

Draw the normal distribution curve

Step 4

`P(x\text{ > 6.9\rparen = p\lparen z >2\rparen = 0.4772}`

Final answer

0.4772 x 100

= 47.72%