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((x-\mu)/(\sigma)\leq(65-79)/(7)) \\ =P(z\leq(-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`