If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?
A) 71.76
B) 67.96
C) 61.96
D) 48.24
E) 54.99

Question

Quizplus · Accepted Answer

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values: $1.96 = \frac{x - 60}{6}$. Solving for $x$ gives $x = 1.96 \times 6 + 60 = 11.76 + 60 = 71.76$.

If the Z-Value for a Given Value X of the Random