Answer :
a) The 85th percentile value for the IELTS score is 10.12.
b) About 62.21% of the students will not qualify for admission based on their IELTS score.
a.
The median of a normal distribution is equal to its mean, which is given as 7.
Therefore, the median IELTS score is 7.
To find the 85th percentile value, we need to find the IELTS score that corresponds to the z-score of 1.04, since the area to the left of this z-score is 0.85.
Using the formula z = (x - μ) / σ, we can solve for x:
1.04 = (x - 7) / 3
x - 7 = 3.12
x = 10.12
Therefore, the 85th percentile value for the IELTS score is 10.12.
b.
Using the z-scores corresponding to these scores, we get:
z₁ = (6 - 7) / 3
= -0.33
z₂ = (9 - 7) / 3
= 0.67
As per the standard normal distribution table,
P(z < -0.33) = 0.3707
P(z > 0.67) = 0.2514
Therefore, the probability that a randomly selected student will not qualify for admission is:
P(not qualified) = P(z < -0.33) + P(z > 0.67)
= 0.3707 + 0.2514
= 0.6221
This means that about 62.21% of the students will not qualify for admission based on their IELTS score.
Learn more about probability here:
brainly.com/question/11234923
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