Prompt According to the College Board website, the scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and standard deviation of 111. Assume that SAT-M scores have a normal probability distribution. One of the criteria for admission to a certain engineering school is an SAT-M score in the 98th percentile. This means the score is in the top 2% of scores. Find the actual SAT-M score marking the 98th percentile?

The actual SAT-M score marking the 98th percentile is 735.105.

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:

Find the actual SAT-M score marking the 98th percentile?

This is the value of X when Z has a pvalue of 0.98. So it is X when Z = 2.055.

The actual SAT-M score marking the 98th percentile is 735.105.

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

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step-by-step explanation:

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