Question

ACT math scores for a particular year are approximately normally distributed with a mean of 28 and a standard deviation of 2.4.​Part
A: What is the probability that a randomly selected score is greater than 30.4?




Part B: What is the probability that a randomly selected score is less than 32.8?



Part C: What is the probability that a randomly selected score is between 25.6 and 32.8?
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Answer 1

Answer:

$a. \ \ \ P(X>30.4)=0.1587\\\\b. \ \ \ P(X$

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:

$z=\frac{\bar X-\mu}{\sigma}$

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

$P(X>30.4)=P(z$

$P(X>)=P(z>\frac{\bar X-\mu}{\sigma})\\\\z=\frac{30.4-28}{2.4}=1.0\\\\\therefore P(z>1)=1-0.84134\\\\=0.1587$

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

$P(X$

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

$P(25.6$

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