Final answer:
To find the probability that a randomly selected value is between 117.2 and 219.4 from a normal distribution with a mean of 61 and a standard deviation of 51.1, we can standardize the values and use a standard normal distribution table or calculator.
Step-by-step explanation:
To find the probability that a randomly selected value is between 117.2 and 219.4, we can use the standard normal distribution.
First, we need to standardize the values using the formula:
Z = (x - μ) / σ
Where x is the value, μ is the mean, and σ is the standard deviation.
For 117.2:
Z1 = (117.2 - 61) / 51.1 = 1.1085
For 219.4:
Z2 = (219.4 - 61) / 51.1 = 3.4961
Next, we can use a standard normal distribution table or a calculator to find the probability between these two Z scores.