Answer:
0.17 is the probability that X takes a value less than 158.
Step-by-step explanation:
We are given the following in the question:
Mean = 169
The variable X is normally distributed.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]P(x > 180) = 0.17[/tex]
[tex]P( X > 180) = P( z > \displaystyle\frac{180 - 169}{\sigma})=0.17[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{11}{\sigma})=0.17 [/tex]
[tex]=P( z \leq \displaystyle\frac{11}{\sigma})=0.83 [/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{11}{\sigma} = 0.954\\\\\sigma = 11.53[/tex]
We have to evaluate
P(x < 158)
[tex]P( x < 158) = P( z < \displaystyle\frac{158- 169}{11.53}) = P(z < -0.954)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 158) = 0.170[/tex]
0.17 is the probability that X takes a value less than 158.
