Answer:

Step-by-step explanation:
a. Given that the mean is 28 and the standard deviation is 2.4.
Let X be the score of our random selection.
-The z-score is calculated using the formula:

-The probability that the score is greater than 30.4 is calculated as:


Hence, the probability of a random score being greater than 30.4 is 0.1587
b. The probability that a randomly selected score is less than 32.8:
Mean=28, sd=2.4 and X=32.8

Hence, the probability that a random selection has a score less than 32.8 is 0.9773
c. The probability that a randomly selected score is between 25.6 and 32.8:
mean=28, sd=2.4 X=25.6, 32.8

Hence, the probability of the score being between 25.6 and 32.8 is 0.8186