Answer:
about 4.1%
Step-by-step explanation:
You want to find the probability that the mean of 45 students' scores is 80 or above on the test with scores normally distributed with a mean of 77.2 and a standard deviation of 10.8.
Sample mean standard deviation
The standard deviation of the sample mean is the population standard deviation divided by the root of the sample size. Here, the means of samples of 45 students will have a standard deviation of ...
10.8/√45 ≈ 1.60997
Probability
The probability that the mean will be above 80 is the probability of a z-score above ...
(80 -77.2)/1.60997 ≈ 1.739
That probability is ...
P(Z > 1.739) ≈ 4.1%
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Additional comment
The use of your Casio 9570 calculator is described with examples in its software manual, available from Casio customer support. Stat functions can be selected from a menu, and Normal CDF functions from another menu under that.
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