Final answer:
To find the probability that a single randomly selected value is between 154.1 and 172.1 in a normal distribution with mean 163.7 and standard deviation 45.1, we can calculate the z-scores for each value and use the standard normal distribution table or calculator to find the probability between these z-scores.
Step-by-step explanation:
To find the probability that a single randomly selected value is between 154.1 and 172.1, we need to calculate the z-scores for these values. The z-score formula is given by z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
Using the given values of μ = 163.7 and σ = 45.1, we can calculate the z-score for 154.1 as z1 = (154.1 - 163.7) / 45.1 = -0.213 and the z-score for 172.1 as z2 = (172.1 - 163.7) / 45.1 = 0.185.
Next, we use a standard normal distribution table or a calculator to find the area/probability between these z-scores. Subtracting the probability corresponding to the smaller z-score from the probability corresponding to the larger z-score gives us the desired probability.