Question

provide an appropriate response. use the standard normal table to find the probability. iq test scores are normally distributed with a mean of 95 and a standard deviation of 13. an individuals iq score is found to be 102. find the z - score corresponding to this value. round the answer to the nearest hundredth.

a. -0.54
b. -1.86
c. 1.86
d. 0.54

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Substitute given values

We are given that $x = 102$, $\mu=95$, and $\sigma = 13$. Substitute these values into the formula: $z=\frac{102 - 95}{13}=\frac{7}{13}\approx0.54$.

Answer:

D. 0.54