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Answer :
Final Answer:
The indicated 1st quartile (Q1) score based on a normal distribution with a mean of 100 and a standard deviation of 15 is C) 93.4.
Explanation:
To find the 1st quartile (Q1) in a normal distribution, we first need to determine the z-score corresponding to the 25th percentile (since Q1 represents the 25th percentile). The z-score formula is given by:
[tex]\[Z = \frac{X - \mu}{\sigma}\][/tex]
Where:
Z = Z-score
X = The value we want to find (Q1)
μ (mu) = Mean (100 in this case)
σ (sigma) = Standard deviation (15 in this case)
For the 25th percentile, Z = -0.6745 (you can look this up in a standard normal distribution table). Now, we can rearrange the formula to find X (Q1):
[tex]\[X = Z * σ + μ\][/tex]
Substituting the values:
X = (-0.6745) * 15 + 100 = 93.3875
Rounded to one decimal place, the 1st quartile score is approximately 93.4. Option C is correct.
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