Pulse Rates. In Exercises 13–24, use the data in the table bel...

Question

Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.

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Find the probability that a male has a pulse rate between 70 beats per minute and 90 beats per minute.

Accepted Answer

Welcome back, everyone. In this problem, find the probability that a male has a height between 160 and 190 centimeters. Given that the distribution of heights for males is normal with a mean of 175 centimeters and a standard deviation of 6 centimeters. A says it's 0.0062, B 0.0124, C is 0.9938, and D 0.9876. Now, let's first make note of the information we have, OK? So far we know that we want to find the probability that a male has a height between 160 and 190 centimeters. So we can say that our lower bound, our lower limit X1 is 160 centimeters and our upper limit X2 is 190 centimeters. We also know that our distribution is normal. This is very important. And it has a mean mule of 175 centimeters while a standard deviation of 6 centimeters. So how can we find or how can we use this information to find the probability? That the height is between 160 centimeters and 190 centimeters. Well, because it's normal, OK, then we could first figure out what the probability is using the standard normal distribution. In other words, We can find from the probability that X is between X1 and X2. The probability that X is, sorry, that Z or Z score is between the corresponding Z1 and Z2 scores for our table or for our values, OK? Now, how do we find the Z score? Well, the Z score or the Z value is going to be equal to X minus the mean mu divided by the standard deviation sigma. So if we can find the Z scores for X1 and X2 respectively, we should be able to use that to find the probability using the standard normal distribution because no, this implies then. The Z1 is going to be equal to 160 minus 175 divided by 6, and that's -15 divided by 6 or -2.5. Likewise, Z2 will be equal to X2, 190 minus 175 divided by 6, and that's 15 divided by 6 which equals 2.5. So What this tells us then. Is that we are looking for the probability. OK, that Z. Is between -2.5 and 2.5 because this corresponds with the probability it's between 160 and 190 centimeters. Now what is that Z score going to be? Well, We know that this is going to be equal to the probability that Z is less than 2.5. Minus the probability that Z is less than -2.5. If we refer to our standard normal distribution table, the probability Z is less than 2.5 0.9938, while the probability it's less than -2.5 is 0.0062. So now by calculating this probability, we should get it by subtracting to be 0.9876. What does that mean? Well, this tells us that the probability a male has a height between 160 and 190 centimeters is approximately 0.9876. If we look back at our answer choices, that means D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.

Find the probability that a male has a pulse rate between 70 beats per minute and 90 beats per minute.

Key Concepts

Normal Distribution

Mean and Standard Deviation

Probability Calculation

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Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.Find the probability that a male has a pulse rate between 70 beats per minute and 90 beats per minute.