for a math proficiency exam, it is known that the population mean score is 1100 and the population standard deviation is 100. if the test is administered to 64 randomly selected individuals from this population, what is the probability that the sample mean will lie between 1070 and 1120? after finding the appropriate probability, indicate the interval that includes this probability. group of answer choices .7001 to .8500 .6001 to .7000 .8501 to 1.000 .0000 to .3000 .3001 to .6000

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15-12-2022
Mathematics

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for a math proficiency exam, it is known that the population mean score is 1100 and the population standard deviation is 100. if the test is administered to 64 randomly selected individuals from this population, what is the probability that the sample mean will lie between 1070 and 1120? after finding the appropriate probability, indicate the interval that includes this probability. group of answer choices .7001 to .8500 .6001 to .7000 .8501 to 1.000 .0000 to .3000 .3001 to .6000

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-21T08:08:59+01:00

The probability that the sample mean will lie between 1070 and 1120 is .7001 to .8500.

To find the probability that the sample mean will lie between 1070 and 1120, we use the Z-score formula:

Z = (x - μ) / σ

where x is the value we are looking for (in this case 1070 or 1120), μ is the population mean (1100), and σ is the population standard deviation (100).

Using this formula, we can calculate the Z-scores for 1070 and 1120, which are -0.3 and 0.2 respectively.

We can then use a Z-table to find the probability associated with each of these Z-scores. The probability associated with a Z-score of -0.3 is 0.6179, and the probability associated with a Z-score of 0.2 is 0.7886.

The probability that the sample mean will lie between 1070 and 1120 is the difference between these two probabilities, which is 0.1707. This is equivalent to a probability of 0.7001 to 0.8500.

Learn more about probability here

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