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 the density function to find the probability that X takes a value less than 158

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:

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

We have to evaluate

P(x < 158)

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

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

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743