Question

Amanda earned a score of 940 on a national achievement test that was normally distributed. The mean test score was 850 with a standard deviation of 100. If 1000 students took the test, how many scored below Amanda? Use your z table.

Question 7 options:

320


820


180


100

Answer 1

@boldjon

Answer 2

@sleepingwithsirens1

Answer 3

Um, I think the answer is D 100

Answer 4

thnxs

Answer 5

To solve this question, you'll need to use a table of the standardized Normal distribution. Fortunately, you can just use a graphing calculator, or you can find a Normal distribution calculator on the internet. It'll ask for the three facts from your question. (If the calculator also asks for cumulative probability, leave that blank because that's what you're trying to solve for.)
Standard score 940
Mean 850
Standard deviation 100

So, the answer will be the cumulative probability, which will be a number with a few decimals. However, this represents the students who had a LOWER score than Amanda. You'll need to subtract this from 1 in order to get the opposite number, the proportion of students who had a higher score than Amanda. Be sure to multiply the result by 100 to get a percentage. That's it.

Here's some additional info that might help explain the approach. The first step to solving this question is to figure out the difference between Amanda's score and the mean score: 940 minus 850 is 90. This tells us how different her score was from the average.
Since the standard deviation is 100, we know that Vivian's difference (90) is within one standard deviation from the mean. In other words, if you increase the mean by one standard deviation, 850 + 100, you get 950, and you can see that Vivian's score of 940 doesn't get that high. Specifically, her difference of 90 is 90% of the standard deviation of 100. The decimal equivalent of 90% is 0.90, and this is called Vivian's z-score.In math notation, we've done this: z = (X - μ) / σ = (940 - 850) / 100 = 0.90 In math notation, we've done this: z = (X - μ) / σ = (940 - 850) / 100 = 0.90.

As you may know, in a normal distribution it's expected that about 68% of all observations will fall within 1 standard deviation of the mean, 95% will fall within 2 standard deviations, and 99% will fall within 3 standard deviations. You now have all the info you need to do a rough calculation of the cumulative probability. Here's how to put it together:

The upper half of the 68% (the scores between the mean and the first standard deviation) = 34%

Vivian's 90% of the 34% = 30.6%
All the test scores lower than the mean = 0.500 (this is 1/2 of all test scores)
+ All the test scores between the mean and Vivian's score = 0.306 (see above)
= 0.806, which is not the real cumulative probability, but an approximation.

Answer 6

so d right

Answer 7

Yes

Answer 8

thnxs man wanna ask another question so i can give u a medal this time

Answer 9

Don't worry about medals :)

Answer 10

The lifetimes of 20,000 light bulbs are normally distributed. The mean lifetime is 230 days. The standard deviation is 40 days. Find the values defined by the standard deviation in a normal distribution for 3 standard deviations

110 to 350


230 to 350


150 to 310


230 to 310

Answer 11

You are welcome Milliaun. Did this help? Becuase to solve you just subtract all values and then you get 100.

Answer 12

yes thnks @ScaryPumpkins

Answer 13

oh i think its a