Significant Values. In Exercises 9–12, use the range rule of t...

Question

Significant Values. In Exercises 9–12, use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high.

IQ Scores The Wechsler test is used to measure intelligence of adults aged 16 to 80. The mean test score is 100 and the standard deviation is 15.

IQ Scores The Wechsler test is used to measure intelligence of adults aged 16 to 80. The mean test score is 100 and the standard deviation is 15.

Accepted Answer

Welcome back, everyone. In this problem, a study measured the resting heart rates in beats per minute of a group of healthy adults. The mean resting heart rate was 72 BPM with a standard deviation of 10 BPM. Use the range rule of thumb to identify first, the values that are significantly low. Second, the values that are significantly high, and the third, the values that are neither significantly low nor significantly high. A says that values below 92 bpm are significantly low. Values above 52 bpm are significantly high, and 72 BPM is a value that's neither significantly low nor significantly high. B says below 52, above 92, and between 52 and 92 respectively. C says below 52, above 92, and 72 and D says below 45, above 100 and between 45 and 100. No How are we going to figure out which values are low and high and which ones are in between? Well, notice our problem statement gives us an idea. We're supposed to use the range rule of thumb. What does that mean? Well, this rule states that most values about 95% lie within two standard deviations of the mean. OK. So by the range rule of thumb. OK. By that rule. Then we know that values. Below, OK. Vars below. Or mean minus 2 standard deviations, 2 sigma, OK. Are significantly low. OK. So in our problem here. Notice that we were told the mean resting heart rate mule is 72 BPM. Well, our standard deviation sigma is 10 bpm. So what does that mean using our rule of thumb? Well, no, this would imply then that. 72 bpm or values below 72 bpm minus 2 multiplied by 10 bpm would be significantly low. 2 multiplied by 10 is 20 and 72 minus 20 equals 52. So this means that values below 52 bpm are going to be significantly low. Now, we also know that it tells us that values above, OK, or mean +2 standard deviations then are going to be significantly high. So in that case, OK, this would imply then that values that are. 72 or greater than 72 + 2 multiplied by 10 are going to be significantly high. That's 72 + 20, which is 92 BPM. Thus, values above 92 BPM are going to be significantly high. Now which ones are neither significantly low nor significantly high? Well, it would be everything in between. Therefore, values below 52 BPM are significantly low, values above 92 BPM are significantly high, and values between 52 and the 92 BPM are neither significantly low nor high. If we look at our answer choices, that means B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Key Concepts

Mean

Standard Deviation

Range Rule of Thumb

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