Let $x$ be a random variable that is normally distributed with the given mean $\mu = 48$ and standard deviation $\sigma = 8$ . Find the probability $P ( x 55 )$ using a symbolic integration utility. Round your answer to four decimal places.
A)0.2525
B)0.1908
C)0.3085
D)0.0763
E)0.1223

Question

Let $x$ be a random variable that is normally distributed with the given mean $\mu = 48$ and standard deviation $\sigma = 8$ . Find the probability $P ( x > 55 )$ using a symbolic integration utility. Round your answer to four decimal places.
A)0.2525
B)0.1908
C)0.3085
D)0.0763
E)0.1223

Quizplus · Accepted Answer

To find $P(x > 55)$ for a normally distributed variable with $\mu = 48$ and $\sigma = 8$, we first calculate the z-score for $x = 55$: $z = \frac{55 - 48}{8} = \frac{7}{8} = 0.875$. Using the standard normal distribution table or a calculator, the probability of $z > 0.875$ is approximately 0.1908. This means the probability $P(x > 55)$ is 0.1908.

Let xxx Be a Random Variable That Is Normally Distributed with the with the Given

Let $x$ Be a Random Variable That Is Normally Distributed with the with the Given