Question

Let X be a normal random variable with a mean of 7.6 and a standard deviation of 3. We want to find a value "a" such that the probability that X is greater than "a" is approximately 0.73.

Find the value of "a" up to 4 decimal places.

Answer 1

To find the value of "a", convert the given probability to a Z-score using the standard normal distribution, then apply the formula using the mean and standard deviation of X to get "a".

Step-by-step explanation:

The student is asking to find the value of "a" such that probability that a normal random variable X is greater than "a" is approximately 0.73, given that X has a mean of 7.6 and a standard deviation of 3. This can be accomplished by using a standard normal distribution table or a Z-score calculator to find the Z-score that corresponds to the cumulative probability of 0.27 (since 1 - 0.73 = 0.27). Once the Z-score is found, the value of "a" can be calculated using the formula X = μ + Zσ, where μ is the mean and σ is the standard deviation.