A population of values has a normal distribution with $U=147.3$ and $O=66.4$ You intend to draw a random sample of size $n=66$ Find the probability that a single randomly selected value is between 144 and 153.8.|

Step 1 ：We are given a population of values that follows a normal distribution with a mean (U) of 147.3 and a standard deviation (O) of 66.4. We are asked to find the probability that a single randomly selected value is between 144 and 153.8.

Step 2 ：We can solve this problem by using the Z-score formula, which standardizes a value to the standard normal distribution (mean = 0, standard deviation = 1). The Z-score formula is: \(Z = \frac{X - U}{O}\), where X is the value, U is the mean, and O is the standard deviation.

Step 3 ：We need to calculate the Z-scores for both 144 and 153.8. Let's start with 144: \(Z1 = \frac{144 - 147.3}{66.4} = -0.04969879518072306\).

Step 4 ：Next, we calculate the Z-score for 153.8: \(Z2 = \frac{153.8 - 147.3}{66.4} = 0.09789156626506024\).

Step 5 ：The probability we are looking for is the area under the standard normal curve between these two Z-scores. This area represents the probability that a single randomly selected value from this population will fall between 144 and 153.8. The probability is approximately 0.05880959322560908.

Step 6 ：Final Answer: The probability that a single randomly selected value is between 144 and 153.8 is approximately \(\boxed{0.0588}\).