Solve the problem.
-Scores on a test are normally distributed with a mean of $65.3$ and a standard deviation of $10.3$. Find P81, which separates the bottom $81 \%$ from the top $19 \%$.
A)68.3
B)0.291
C)74.4
D)0.88

Question

Quizplus · Accepted Answer

To find P81, which is the score that separates the bottom 81% from the top 19%, we use the Z-score formula and the normal distribution properties. The Z-score corresponding to 81% in the standard normal distribution table is approximately 0.88. We then use the formula for converting a Z-score to an actual score in a distribution: $X = \mu + Z\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $Z$ is the Z-score. Plugging in the values, we get $X = 65.3 + 0.88 \times 10.3 \approx 74.4$.

Solve the Problem 65.365.365.3 And a Standard Deviation Of 10.310.310.3 Find P81, Which Separates the Bottom

Solve the Problem $65.3$ And a Standard Deviation Of $10.3$ Find P81, Which Separates the Bottom