Question 7, 5.2.10-T HW Score: $41.07 \%, 5.75$ of 14 points Part 1 of 4 Points: 0 of 1 In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 21.9 and a standard deviation of 6.2 . Complete parts (a) through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 20. The probability of a student scoring less than 20 is (Round to four decimal places as needed.)

Step 1 ：The problem is asking for the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 20. This is a problem of normal distribution. We know that the mean (μ) is 21.9 and the standard deviation (σ) is 6.2.

Step 2 ：We can use the Z-score formula to find the Z-score for a score of 20, which is Z = (X - μ) / σ. Substituting the given values, we get Z = (20 - 21.9) / 6.2 = -0.3064516129032256.

Step 3 ：Then, we can use the cumulative distribution function (CDF) of the standard normal distribution to find the probability that a score is less than 20. The CDF gives the probability that a random variable is less than or equal to a certain value.

Step 4 ：Using the calculated Z-score, we find that the probability is approximately 0.3796. This means that about 37.96% of students are expected to score less than 20 on the reading portion of the test.

Step 5 ：Final Answer: The probability of a student scoring less than 20 is \(\boxed{0.3796}\).