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22. Given 𝜇 = 180 and 𝜎 = 15 in a college entrance examination, find the corresponding z-value ofthe score of the students if 𝑋 = 150.A. 2 B. -2 C. 2.5 D. -2.5______23. From the given in number 12, what is the z-value if X = 200?A. 1.33 B. 1.66 C. 1.99 D. 2.22______24. What is the value of 70th percentile?A. 0.13 B. 0.23 C. 0.52 D. 0.71______25. What is the value of 82nd percentile?A. 0.92 B. 0.83 C. 0.53 D. 0.23II. TRUE OR FALSE. Write TRUE if the statement is correct and FALSE if otherwise. Write your answer in thespace provided before the number. (10 points)___________ 1. The normal distribution characterizes what is typical for a given set of data.___________ 2. All the values for a normal variable are close to the mean.___________ 3. A normal distribution has a mean that is equal to the standard deviation.___________ 4. The normal curve is a bell-shaped curve symmetric about the mean.___________ 5. In a normal distribution, the mean, median, and mode are the same.___________ 6. The standard deviation precisely describes the spread of the normal curve.___________ 7. A normal curve gradually tapers off to values closer and closer to 0 on both sides of the curve.___________ 8. A larger mean value corresponds to a wider normal curve.___________ 9. The maximum point of a normal curve occurs at the median of the distribution.___________ 10. The area under the normal curve to the right of the mean is 0.5

Question

  1. Given 𝜇 = 180 and 𝜎 = 15 in a college entrance examination, find the corresponding z-value ofthe score of the students if 𝑋 = 150.A. 2 B. -2 C. 2.5 D. -2.5______23. From the given in number 12, what is the z-value if X = 200?A. 1.33 B. 1.66 C. 1.99 D. 2.22______24. What is the value of 70th percentile?A. 0.13 B. 0.23 C. 0.52 D. 0.71______25. What is the value of 82nd percentile?A. 0.92 B. 0.83 C. 0.53 D. 0.23II. TRUE OR FALSE. Write TRUE if the statement is correct and FALSE if otherwise. Write your answer in thespace provided before the number. (10 points)___________ 1. The normal distribution characterizes what is typical for a given set of data.___________ 2. All the values for a normal variable are close to the mean.___________ 3. A normal distribution has a mean that is equal to the standard deviation.___________ 4. The normal curve is a bell-shaped curve symmetric about the mean.___________ 5. In a normal distribution, the mean, median, and mode are the same.___________ 6. The standard deviation precisely describes the spread of the normal curve.___________ 7. A normal curve gradually tapers off to values closer and closer to 0 on both sides of the curve.___________ 8. A larger mean value corresponds to a wider normal curve.___________ 9. The maximum point of a normal curve occurs at the median of the distribution.___________ 10. The area under the normal curve to the right of the mean is 0.5
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Solution

  1. To find the z-value, we use the formula z = (X - μ) / σ. Substituting the given values, we get z = (150 - 180) / 15 = -2. So, the answer is B. -2.

  2. Using the same formula, z = (200 - 180) / 15 = 1.33. So, the answer is A. 1.33.

  3. The value of the 70th percentile in a standard normal distribution is approximately 0.52. So, the answer is C. 0.52.

  4. The value of the 82nd percentile in a standard normal distribution is approximately 0.92. So, the answer is A. 0.92.

TRUE OR FALSE:

  1. TRUE. The normal distribution does characterize what is typical for a given set of data.

  2. FALSE. Not all values for a normal variable are close to the mean. They are spread out around the mean.

  3. FALSE. The mean and standard deviation are different measures and are not necessarily equal in a normal distribution.

  4. TRUE. The normal curve is a bell-shaped curve symmetric about the mean.

  5. TRUE. In a normal distribution, the mean, median, and mode are the same.

  6. TRUE. The standard deviation describes the spread of the normal curve.

  7. TRUE. A normal curve gradually tapers off to values closer and closer to 0 on both sides of the curve.

  8. FALSE. A larger mean value does not correspond to a wider normal curve. The width of the curve is determined by the standard deviation.

  9. TRUE. The maximum point of a normal curve occurs at the median of the distribution.

  10. TRUE. The area under the normal curve to the right of the mean is 0.5.

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