Final answer:
The correct method to calculate P(X > 30) for the given normal distribution is by converting X to a Z-score and using the standard normal distribution to find the probability.
Step-by-step explanation:
The probability that a normally distributed random variable with a mean µ = 20 and standard deviation σ = 4 exceeds the value 30. To calculate P(X > 30), one would typically use the standard normal distribution table or a calculator with normal probability functions. However, the given reference formula appears incorrect as it suggests the use of the wrong mean (34) and standard deviation (1.5).
To correctly answer this question, you need to standardize the variable by calculating the Z-score, which is given by Z = (X - µ) / σ. This transforms the probability to P(Z > (30 - 20) / 4) = P(Z > 2.5). The Z-score helps us compare this to a standard normal distribution, where µ = 0 and σ = 1.
Use a Z-table or statistical calculator to find P(Z > 2.5), which reveals the desired probability of X being greater than 30 in our original distribution. It's also worth noting that using the clt to find probability refers to utilizing the Central Limit Theorem, which does not directly apply to this individual calculation since we're not dealing with sample means.