Question

Can I please get help on this question. This is from a test I did and I got the answer wrong and would like to know how to work it out so that I know what to do next time

Answer 1

The probability of x<5 is given by the formula:

$P(X<5)=P(Z<\frac{x-\mu}{\sigma})$

Where:

$\begin{gathered} \mu\colon\operatorname{mean} \\ \sigma\colon\text{ standard deviation} \\ x=5 \end{gathered}$

We already know that P(X<5) =0.0228

By replacing these values, we can solve for the mean as follows:

$0.0228=P(Z<\frac{5-\mu}{1})$

If we check in a standard normal table, 0.0228 corresponds to a z-score of -2.00:

Then, Z=-2.00

Replace this value and solve for the mean:

$\begin{gathered} -2=\frac{5-\mu}{1} \\ -2\cdot1=5-\mu \\ -2=5-\mu \\ \text{Add }\mu\text{ to both sides} \\ -2+\mu=5-\mu+\mu \\ -2+\mu=5 \\ \text{Add 2 to both sides} \\ -2+\mu+2=5+2 \\ \mu=7 \end{gathered}$

Then, the answer is 7.