Question

What is F(10) for X, the number of sales in a given day at a store, following a normal distribution with mean (μ) = 10 and standard deviation (σ) = 5?

Answer 1

To find F(10), calculate the probability of getting a value of X less than or equal to 10 in a normal distribution with mean (μ) = 10 and standard deviation (σ) = 5. Using the z-score formula, calculate the z-score for X = 10. Find the cumulative probability associated with the z-score to determine F(10).

Step-by-step explanation:

To find F(10), we need to calculate the probability of getting a value of X less than or equal to 10 in a normal distribution with mean (μ) = 10 and standard deviation (σ) = 5.

To calculate this probability, we need to standardize the value of X using the z-score formula: z = (X - μ) / σ.

Using the given values, we substitute X = 10, μ = 10, and σ = 5 into the formula and calculate the z-score:

z = (10 - 10) / 5 = 0.

Next, we need to find the cumulative probability associated with the z-score using a standard normal table or a calculator. The cumulative probability represents the area under the normal distribution curve up to the given z-score. In this case, since z = 0, the cumulative probability is 0.5.

Therefore, F(10) = 0.5.