Chapter 9, Problem T9.10SPT

To determine

To find: the following has the greatest probability.

Answer to Problem T9.10SPT

P (Z<2) if z is a standard normal random variable

Explanation of Solution

Find the corresponding probability $P\left(z>2\right)$ and $P\left(z<2\right)$ using the normal probability table

  $\begin{array}{c}P\left(z>2\right)=1-P\left(z<2\right)\\ =1-0.9772\\ =0.0228\end{array}$

The probability $P\left(t>2\right)$ at 2 degrees of freedom is the number (or interval) in the column title of the Student’s T table in the appendix that contains the t-value 2 in the row $df=5$ .

  $0.05<P\left(t>2\right)<0.10$

Although the total probability requires to be P(t<2) is 0.95 when P(t>2) is 0.05 and P(t<2) is

0.90 when P (t>2) is 0.10

  $0.90<P\left(t<2\right)<0.95$

The probability $P\left(t>2\right)$ at 2 degrees of freedom is the number (or interval) in the column title of the Student’s T table in the appendix that contains the t-value 2 in the row $df=2$ .

  $0.05<P\left(t>2\right)<0.10$

It is observed that the highest probability is $P\left(z<2\right)=0.9772$ .

Hence, the correct option is (e)