Question

Normal Distribution Value:

Suppose x is a normally distributed random variable with = 48 and = 5. Find a value x₀ of the random variable x that satisfies the following e

Answer 1

To find the value x₀ of a normally distributed random variable, with a mean of 48 and standard deviation of 5, that satisfies a certain condition, we can use the Empirical Rule. About 68 percent of the values lie within one standard deviation of the mean, allowing us to determine x₀ as either 43 or 53.

Step-by-step explanation:

The given question is asking for a specific value, x₀, of a normally distributed random variable. To find this value, we need to use the properties of the normal distribution. The mean, μ, is given as 48 and the standard deviation, σ, is given as 5. We can use the Empirical Rule to determine the range of values within one standard deviation of the mean. About 68 percent of the values lie within one standard deviation of the mean, so we can use this information to find x₀.

To find x₀, we can use the formula:

x₀ = μ ± σ

Substituting the given values, we get:

x₀ = 48 ± 5

Simplifying, we have two possible values for x₀:

x₀ = 43 or x₀ = 53

Therefore, the two values for x₀ that satisfy the given condition are 43 and 53.