The final exam scores for History 101 are at the University of Oklahoma are normally distributed with mean p = 73.4 and standard deviation o = 8.2, use the Z scores and Z areas table to find the following: If 1 student is randomly selected, find the probability that the student scored an A (90 or above) on the exam. 18 (A) 0.9783 (B) 0.9673 (C) 0.0864 (D) 0.0217 X scor H= 73.4 O = 8.2 Z scal z = 0 If 1 student is randomly selected, find the probability that the student scored an F (59 or below) on the exam. 19 (A) 0.9608 (B) 0.0392 (C) 0.6380 (D) 0.7642 If a sample of 25 students are randomly selected, find the probability that the mean of their test scores was 75 or below. 20 (A) 0.9306 (B) 0.8298 (C) 0.8340 (D) 0.7506

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**Using the Standard Normal Distribution Z Scores**

The final exam scores for History 101 at the University of Oklahoma are normally distributed with a mean (μ) = 73.4 and standard deviation (σ) = 8.2. Use the Z scores and the Z areas table for the following problems:

18. **If 1 student is randomly selected, find the probability that the student scored an A (90 or above) on the exam.**

   - (A) 0.9783
   - (B) 0.9673
   - (C) 0.0864 *(Correct Answer)*
   - (D) 0.0217

19. **If 1 student is randomly selected, find the probability that the student scored an F (59 or below) on the exam.**

   - (A) 0.9608
   - (B) 0.0392
   - (C) 0.6380
   - (D) 0.7642

20. **If a sample of 25 students are randomly selected, find the probability that the mean of their test scores was 75 or below.**

   - (A) 0.9306
   - (B) 0.8298
   - (C) 0.8340 *(Correct Answer)*
   - (D) 0.7506

**Explanation of the Graph:**

The graph shown is a standard bell curve representing the normal distribution of the test scores. The horizontal axis represents X scores, and the vertical axis does not have specific values but indicates frequency. 

- The mean (μ = 73.4) is the center of the distribution.
- The standard deviation (σ = 8.2) shows how spread out the scores are from the mean.
- The Z scale is marked at z = 0 at the mean, indicating the standard score.
Transcribed Image Text:**Using the Standard Normal Distribution Z Scores** The final exam scores for History 101 at the University of Oklahoma are normally distributed with a mean (μ) = 73.4 and standard deviation (σ) = 8.2. Use the Z scores and the Z areas table for the following problems: 18. **If 1 student is randomly selected, find the probability that the student scored an A (90 or above) on the exam.** - (A) 0.9783 - (B) 0.9673 - (C) 0.0864 *(Correct Answer)* - (D) 0.0217 19. **If 1 student is randomly selected, find the probability that the student scored an F (59 or below) on the exam.** - (A) 0.9608 - (B) 0.0392 - (C) 0.6380 - (D) 0.7642 20. **If a sample of 25 students are randomly selected, find the probability that the mean of their test scores was 75 or below.** - (A) 0.9306 - (B) 0.8298 - (C) 0.8340 *(Correct Answer)* - (D) 0.7506 **Explanation of the Graph:** The graph shown is a standard bell curve representing the normal distribution of the test scores. The horizontal axis represents X scores, and the vertical axis does not have specific values but indicates frequency. - The mean (μ = 73.4) is the center of the distribution. - The standard deviation (σ = 8.2) shows how spread out the scores are from the mean. - The Z scale is marked at z = 0 at the mean, indicating the standard score.
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