Question

Suppose a normal distribution has a mean of 89 and a standard deviation of7. What is P(x less than or equal to 82)?A. 0.16B. 0.84C. 0.025D. 0.975

Answer 1

In order to find this probability, first let's find the value of z for this case, where:

$z=\frac{x-\mu}{\sigma}$

Using the mean = 89 and the std dev = 7, for x = 82 we have:

$z=\frac{82-89}{7}=-1$

Looking at the z-table for z = -1, we have a value of 0.1587.

So the probability of P(x<=82) is equal to 0.1587 (rounding, we have 0.16).

Therefore the correct option is A.