Questions: Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean 360 and standard deviation 50. What is P(x<400)?

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean 360 and standard deviation 50. What is P(x<400)?

Transcript text: Let the random variable $X$ represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $\$ 360$ and standard deviation $\$ 50$. What is $P(x<\$ 400) ?$

Solution

Solution Steps

Step 1: Define the Random Variable

Let the random variable $ X $ represent the profit made on a randomly selected day by a certain store. It is given that $ X $ follows a normal distribution with mean $ \mu = 360 $ and standard deviation $ \sigma = 50 $.

Step 2: Calculate the Probability

We need to find the probability $ P(X < 400) $. This can be computed using the cumulative distribution function (CDF) of the normal distribution. The result of the calculation shows that:

\[ P(X < 400) \approx 0.7881 \]