In a certain normal distribution, find the mean $\mu$ when ? = 5 and 5.48% of the area lies to the left of 78.
A)86
B)70
C)94
D)62

Question

Quizplus · Accepted Answer

Given that 5.48% of the area lies to the left of 78 in a normal distribution, this corresponds to a Z-score that reflects the 5.48th percentile. Looking up this percentile in a standard normal distribution table or using a calculator, we find that it corresponds to a Z-score of approximately -1.6 (since it's in the lower tail of the distribution). The Z-score formula is $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value in the distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. Rearranging this formula to solve for $\mu$, we get $\mu = X - Z\sigma$. Substituting the given values ($X = 78$, $Z = -1.6$, $\sigma = 5$), we find $\mu = 78 - (-1.6 \times 5) = 78 + 8 = 86$.

In a Certain Normal Distribution, Find the Mean μ\muμ When ? = 5 and 5

In a Certain Normal Distribution, Find the Mean $\mu$ When ? = 5 and 5