Question

Suppose a normal distribution has a mean of 79 and a standard deviation of7. What is P(x < 65)?

Answer 1

Given:

Mean and standard deviation for the normal distribution is,

Mean (μ)=79

Stanadard deviation (σ)=7

For the normal distribution ,

$\begin{gathered} P(x\leq65)=P(\frac{x-\mu}{\sigma}\leq\frac{65-79}{7}) \\ =P(z\leq\frac{-15}{7}) \\ =P(z\leq-2.14) \\ =\text{ value of z- score(-2.14)} \end{gathered}$

According to z-table, the value of z-score (-2.14)=0.016

Hence,

$P(x\leq65)=0.016$