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ACTIVITY NO. 10
The mean height of the learners in Grade 1 Newton is
125 cm and the standard deviation is 3.5 cm . Assuming the
heights are normally, what percent of the height is:
a. Greater than 135 cm ?
b. Less than 128 cm ?
c. Between 115 and 130 cm ?

Ask by Barber Sandoval. in the Philippines
Jan 24,2025

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  • a. 0.21% of learners are taller than 135 cm.
  • b. 80.51% of learners are shorter than 128 cm.
  • c. 92.15% of learners have heights between 115 cm and 130 cm.

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Mind Expander

To find the percentages, we rely on the properties of the normal distribution. First, let’s convert the heights to z-scores using the formula .
a. For 135 cm:

Using the z-table, about 99.86% of the distribution falls below this z-score, so approximately 0.14% are greater than 135 cm.
b. For 128 cm:

Looking up 0.86 in the z-table gives about 0.8133, meaning about 81.33% of learners are less than 128 cm.
c. For heights between 115 cm and 130 cm:
Calculate z-scores for both:
For 115 cm:
(about 0.14% below 115 cm)
For 130 cm:
(about 92.55% below 130 cm)
So, the percentage between 115 cm and 130 cm is .

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