A continuous random variable X has a normal distribution with mean 169. The probability that X takes a value greater than 180 is 0.17. Use this information and the symmetry of t…

Question

asked Mar 26, 2021 31.4k views

1 Answer

Viswanathgs · Answer 1 · 2021-03-30T16:52:28+0000

Answer:

0.17 is the probability that X takes a value less than 158.

Explanation:

We are given the following in the question:

Mean = 169

The variable X is normally distributed.

Formula:

$z_(score) = \displaystyle(x-\mu)/(\sigma)$

P(x > 180) = 0.17

$P( X > 180) = P( z > \displaystyle(180 - 169)/(\sigma))=0.17$

$= 1 -P( z \leq \displaystyle(11)/(\sigma))=0.17$

$=P( z \leq \displaystyle(11)/(\sigma))=0.83$

Calculation the value from standard normal z table, we have,

$\displaystyle(11)/(\sigma) = 0.954\\\\\sigma = 11.53$

We have to evaluate

P(x < 158)

$P( x < 158) = P( z < \displaystyle(158- 169)/(11.53)) = P(z < -0.954)$

Calculation the value from standard normal z table, we have,

P(x < 158) = 0.170

0.17 is the probability that X takes a value less than 158.