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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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

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

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