Gregorio took two tests. find his z-score for each test. (remember: the number of standard deviations between a score and the mean score is indicated by a z-score.) on which did he score better compared with others in his class? test a test b gregorio’s score 62 70 mean score 80 90 standard deviation 6 10 a. test a: 3; test b: 2; test a c. test a: –2; test b: –3; test a b. test a: –3; test b: –2; test b d. test a: –3; test b: –2; test a

As the problem statement tells you,

... z = (x - μ)/σ

When you have multiple calculations of the same type, sometimes it is easier to do the calculation using a spreadsheet or a list. Here, we use a list for the numbers of [testA, testB], so we can put the calculations all in one expression. Math operations are performed on corresponding members of the list.

([62, 70] - [80, 90])/[6, 10]

... = [-18/6, -20/10] = [-3, -2]

-2 > -3, so Gregorio did better on Test B.

The appropriate answer choice is

... b. Test A: –3; Test B: –2; Test B

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

the correct answer is 5 6 and 7