High School

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**WRITTEN WORKS**

**Directions:** Read each item carefully and answer what is being asked. Choose the letter of the correct answer. If the answer is not in the choices, write E instead.

1. What is the proportion of the area to the left of [tex]z = -1.2[/tex]?
- a. .1051
- b. .1151
- c. .1251
- d. .1351

2. Find the proportion of the area between [tex]z = 1[/tex] and [tex]z = 2[/tex].
- a. 11.59%
- b. 12.59%
- c. 13.59%
- d. 14.49%

3. In a medical mission held in Romblon capitol, the distribution of cholesterol readings, in mg/dl, is normally distributed with a mean of 210 and a standard deviation of 12. What is the raw reading if the [tex]z[/tex] value is 2.5?
- a. 210
- b. 220
- c. 230
- d. 240

4. If the mean is 60 and the standard deviation is 8, what is the corresponding [tex]z[/tex] score if the raw score is 72?
- a. 1.5
- b. 2.5
- c. 3.5
- d. 4.5

5. The Intelligence Quotient (IQ) scores for people are normally distributed with a mean of 100 and a standard deviation of 16. If Juan was randomly selected to take the test, what is the probability that her score is between 100 and 120?
- a. .3994
- b. .3995
- c. .3996
- d. .3997

Answer :

Final answer:

These questions cover the application of z-scores in standard normal distributions and include finding proportions of areas, calculating raw readings from z-scores, and determining z-scores from raw scores.

Explanation:

The area to the left of z=-1.2 can be found by looking at a standard normal table or using a z-score calculator, which reveals that the proportion of the area to the left of z=-1.2 is .1151 (option b), not .1051. For the second question, the proportion of the area between z=1 and z=2 is approx.13.59% (option c), as determined via a standard deviation calculator.

For the cholesterol reading, raw reading is detected by adding the value gained from multiplying the z-score to the standard deviation to the mean. Therefore, the raw reading of a z score of 2.5 with a mean of 210 and a standard deviation of 12 is 210 + 2.5*12 = 240 (option d).

Finding a z score given the raw score, mean, and standard deviation can be done using the formula (Raw score - mean) / SD. Thus, the z score for a raw score of 72 with a mean of 60 and a standard deviation of 8 is (72-60)/8 = 1.5 (option a).

Finally, the probability of Juan's IQ score falling between 100 and 120 can be found using a standard normal table. The z-scores corresponding to 100 and 120 (considering the mean=100 and SD=16) are 0 and 1.25 respectively. The area between these z-scores is approximately .3944, so none of the given options are correct.

Learn more about Standard normal distribution here:

https://brainly.com/question/30390016

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