Step 1 :Given that X has a normal distribution with a mean (μ) of 60.0 and a standard deviation (σ) of 4.0, we are asked to find the probability that X is less than 53.0.
Step 2 :First, we calculate the Z-score for X=53.0 using the given mean and standard deviation. The Z-score is calculated as \(Z = \frac{X - \mu}{\sigma}\).
Step 3 :Substituting the given values, we get \(Z = \frac{53.0 - 60.0}{4.0} = -1.75\).
Step 4 :Next, we use a standard normal distribution table to find the probability that X is less than 53.0. The probability corresponding to Z=-1.75 is approximately 0.0401.
Step 5 :This means that there is a 4.01% chance that a randomly selected value from this normal distribution will be less than 53.0.
Step 6 :Final Answer: The probability that X is less than 53.0 is \(\boxed{0.0401}\).