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Answer:
The minimum score required for admission is 21.9.
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 university plans to admit students whose scores are in the top 40%. What is the minimum score required for admission?
Top 40%, so at least 100-40 = 60th percentile. The 60th percentile is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.255. So
The minimum score required for admission is 21.9.
The sum of all the measurements is just the average times the number.
So if the average of all 92 is 7 the sum of those is
The average of the last two is 7.2 so their sum is
That means the sum of the first 90 is
so the average of the first 90 is
cm
So if the average of all 92 is 7 the sum of those is
The average of the last two is 7.2 so their sum is
That means the sum of the first 90 is
so the average of the first 90 is