In a study of
800 men,diastolic blood pressure was found to be approximately normally distributed, with a mean of 84 millimeters (mm) of mercury and standard deviation of 10 millimeters.
Use the 68-95-99.7% rule to determine what percentage of the test group had a diastolic pressure between 74 millimeters
and 94 millimeters of mercury.
It is found that the number of raisins in a box of a popular cereal is normally distributed, with a mean of 133 raisins per box and a standard deviation of 10 raisins. My cereal box has 147 raisins. What is the z-score for this box of cereal?
68%
Jess is right for the first part.
Z = (score-mean)/SD
Insert the values and compute.
Ah, blood pressure, the sneaky way our bodies keep tabs on their internal rollercoaster. Let's crunch some numbers and sprinkle some humor, shall we?
According to the 68-95-99.7% rule, we know that approximately 68% of the data falls within one standard deviation of the mean. So, with a mean of 84 mm and a standard deviation of 10 mm, we can say that roughly 68% of the men had a diastolic pressure between (84-10) and (84+10) millimeters.
That means the range for this 68% chunk is between 74 mm and 94 mm, just like you mentioned. How convenient! So, we can conclude that approximately 68% of the test group had a diastolic pressure in that range.
Well, there you have it! And remember, blood pressure may be serious business, but a little humor never hurts. Just try not to laugh too hard, we don't want your diastolic pressure to skyrocket!
To determine the percentage of the test group with a diastolic pressure between 74 millimeters and 94 millimeters of mercury, we can use the 68-95-99.7% rule, also known as the empirical rule, which applies to approximately normally distributed data.
According to the empirical rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean diastolic blood pressure is 84 millimeters of mercury, and the standard deviation is 10 millimeters of mercury.
First, let's calculate the range within one standard deviation above and below the mean:
Lower boundary = Mean - 1 * Standard deviation = 84 - 1 * 10 = 74 millimeters of mercury
Upper boundary = Mean + 1 * Standard deviation = 84 + 1 * 10 = 94 millimeters of mercury
So, the range of diastolic blood pressure values within one standard deviation of the mean is from 74 to 94 millimeters.
Since the empirical rule tells us that about 68% of the data falls within one standard deviation of the mean, we can conclude that approximately 68% of the 800 men in the study had a diastolic pressure between 74 and 94 millimeters of mercury.
Box of cereal--
You have a mean of 133 raisins with a standard deviation of 10. The cereal box has 147 raisins.
147-133=14
14/10 (Enter fourteen divided by 10 in the calculator)=1.4
The Z score is 1.4.