Learning Task 1.1: Solve for the z-score of the following and identify its area using
the Z-table. (5 points each)
1. The scores in a Probability and Statistics test are normally distributed with a
mean of 25 and standard deviation of 3.5. Andrew got a score of 30.
2. Assume that the weights of apples follow a normal distribution. The mean
weight of apple in grams is 100 and the standard deviation is 15. An apple
is randomly selected having a weight of 115 grams.
3. Assume that the weights of oranges follow a normal distribution. The mean
weight of apple in grams is 140 and the standard deviation is 25. An orange
is randomly selected with a weight of 100 grams.
4. On a nationwide placement test that is normally distributed, the mean was
125 and standard deviation was 15. Your score is 149.
5. Suppose IQ scores are normally distributed with a mean of 100 and
standard deviation of 10. Your IQ is 85.
ANG MAKASAGOT NITO BIBIGYAN KO NG MADAMING POINTS
the Z-table. (5 points each)
1. The scores in a Probability and Statistics test are normally distributed with a
mean of 25 and standard deviation of 3.5. Andrew got a score of 30.
2. Assume that the weights of apples follow a normal distribution. The mean
weight of apple in grams is 100 and the standard deviation is 15. An apple
is randomly selected having a weight of 115 grams.
3. Assume that the weights of oranges follow a normal distribution. The mean
weight of apple in grams is 140 and the standard deviation is 25. An orange
is randomly selected with a weight of 100 grams.
4. On a nationwide placement test that is normally distributed, the mean was
125 and standard deviation was 15. Your score is 149.
5. Suppose IQ scores are normally distributed with a mean of 100 and
standard deviation of 10. Your IQ is 85.
ANG MAKASAGOT NITO BIBIGYAN KO NG MADAMING POINTS
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Answers & Comments
1)
mean = 25
sd = 3.5
raw score
z-score = (raw score - mean)/SD
= (30 - 25)/3.5
= 1.43
2)
mean = 100
sd = 15
raw score = 115
z-score = (raw score - mean)/SD
= (115 - 100)/15
= 1
3)
mean = 140
sd = 25
raw score = 100
z-score = (raw score - mean)/SD
= (100 - 140)/25
= -1.6
4)
mean = 125
sd = 15
raw score = 149
z-score = (raw score - mean)/SD
= (149 - 125)/15
= 1.6
5)
mean = 100
sd = 10
raw score = 85
z-score = (raw score - mean)/SD
= (85 - 100)/10
= -1.5
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