High School

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1. Suppose the distribution of data about the recovered victims of COVID-19 daily has a mean of 145 and a standard deviation of 22. How many standard deviations away from the mean is a value of 79?

A. It is one standard deviation below the mean.
B. It is three standard deviations below the mean.
C. It is two standard deviations above the mean.
D. It is two standard deviations below the mean.

2. The height of SHS students is normally distributed with a mean of 150 cm and a standard deviation of 10 cm. Approximately what percent of these students have a height greater than 140 cm?

A. 80%
B. 84%
C. 86%
D. 88%

3. Find the area above z = 2.56.

A. 0.0052
B. 0.4948
C. 0.9946
D. 0.9948

4. Find the area of the shaded region of the given figure.

A. 0.1587
B. 0.3413
C. 0.3907
D. 0.8413

5. If the weights are normally distributed, what is the z-score of a woman with a weight of 70?

A. -2.5
B. -1.5
C. 1.5
D. 2.5

6. What is the z-score of a woman with a weight of 50 kg?

A. -2.5
B. -1.5
C. 1.5
D. 2.5

7. How many kilograms will correspond to the z-score of 0.5 for the weight of a woman?

A. 56 kg
B. 58 kg
C. 60 kg
D. 62 kg

8. If the average age of retirement for the population in the Philippines is 70 years, with a standard deviation of 5 years, what is the approximate age range in which 68% of people retire?

A. 65–75 years
B. 65–70 years
C. 55–60 years
D. 60–65 years

9. IQ scores of people around the world are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius?

A. 0.83%
B. 3.18%
C. 3.8%
D. 0.38%

Answer :

Let's go through each question step-by-step.


  1. How many standard deviations away from the mean is a value of 79?


    • Given the mean [tex]\mu = 145[/tex] and standard deviation [tex]\sigma = 22[/tex].

    • The formula for the z-score is [tex]z = \frac{X - \mu}{\sigma}[/tex], where [tex]X[/tex] is the value.

    • So, [tex]z = \frac{79 - 145}{22} = \frac{-66}{22} = -3[/tex].

    • Interpretation: The value 79 is three standard deviations below the mean.

    • Correct answer: B. It is three standard deviations below the mean.



  2. Approximately what percent of SHS students have a height greater than 140 cm?


    • Mean height [tex]\mu = 150[/tex] cm and [tex]\sigma = 10[/tex] cm.

    • Find the z-score for 140 cm: [tex]z = \frac{140 - 150}{10} = -1[/tex].

    • Using the standard normal distribution, about 84% of data lies above a z-score of -1.

    • Correct answer: B. 84%



  3. Find the area above [tex]z = 2.56[/tex].


    • From z-tables, [tex]P(Z < 2.56) \approx 0.9946[/tex].

    • Thus, area above [tex]z = 2.56[/tex] is [tex]1 - 0.9946 = 0.0054[/tex].

    • Correct answer: A. 0.0052



  4. Find the area of the shaded region of the given figure.


    • Unfortunately, without the figure, it's not possible to identify the shaded region's area.



  5. If the weights are normally distributed, what is the z-score of a woman with a weight of 70?


    • Assuming mean and standard deviation are provided (need these values to calculate), this step needs these values for a correct z-score calculation.



  6. What is the z-score of a woman with a weight of 50 kg?


    • This requires the mean and standard deviation.



  7. How many kilograms will correspond to the z score of 0.5 of the weight of a woman?


    • Again, the specific mean and standard deviation are needed to calculate the exact weight.



  8. Approximate age range in which 68% of people retire (Philippines)?


    • Mean age [tex]\mu = 70[/tex] years, [tex]\sigma = 5[/tex] years.

    • 68% of data within one standard deviation: [tex]70 - 5 = 65[/tex] to [tex]70 + 5 = 75[/tex].

    • Correct answer: A. 65 – 75 years



  9. What percent of the population is considered genius with IQ [tex]\geq 140[/tex]?


    • Using [tex]\mu = 100[/tex], [tex]\sigma = 15[/tex].

    • Find [tex]z[/tex] for 140: [tex]z = \frac{140 - 100}{15} = 2.67[/tex].

    • From z-tables: [tex]P(Z > 2.67) \approx 0.38%[/tex].

    • Correct answer: D. 0.38%



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