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1 answer:
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Answer:
a) 6.68th percentile
b) 617.5 points
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.
has a pvalue of 0.0668
So this student is in the 6.68th percentile.
b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.
He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.
Answer:
38.5°
Step-by-step explanation:
Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.
The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:
x² = 10² + 8²
x² = 100 + 64
x² = 164
x = √164 = 12.86 yards
For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:
Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule: