assume the body temperature of healthy adults distributed with a mean of 98.20F and a standard deviation of 0.62F. If you have a body temperature of 99.00F, what is your percentile score?
Z = (x-mean)/SD
Insert values and solve for Z.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to that Z score.
99.0-98.2/0.62
Answer = 1.29
Is this correct?
To find the percentile score for a body temperature of 99.00°F, we can use the Z-table.
First, we need to calculate the Z-score, which measures how many standard deviations an observation is from the mean.
The formula to calculate the Z-score is:
Z = (X - μ) / σ
Where:
X = body temperature (99.00°F)
μ = mean (98.20°F)
σ = standard deviation (0.62°F)
Plugging in the values:
Z = (99.00 - 98.20) / 0.62
Z = 0.80 / 0.62
Z ≈ 1.29
Using the Z-table, we can find the percentile score corresponding to a Z-score of 1.29. The percentile score represents the percentage of values below a particular value.
Looking up the value of 1.29 in the Z-table, we can see that it corresponds to a percentile score of approximately 90.72%.
So, if your body temperature is 99.00°F, your percentile score is approximately 90.72%. This means that approximately 90.72% of healthy adults have a lower body temperature than you.
To find your percentile score, we need to determine the percentage of values in the distribution that are below your body temperature of 99.00F.
We can use the standard normal distribution to calculate percentiles. To do this, we need to convert your body temperature to a z-score.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- x is your body temperature (99.00F)
- μ is the mean of the distribution (98.20F)
- σ is the standard deviation of the distribution (0.62F)
Substituting the values:
z = (99.00 - 98.20) / 0.62
z = 0.80 / 0.62
z ≈ 1.29
Now, we can use a z-table or statistical software to find the area under the curve to the left of the z-score 1.29. This area represents the percentage of values below your body temperature.
Using a z-table, we find that the area to the left of 1.29 is approximately 0.8972.
To convert this to a percentile score, we multiply the area by 100:
percentile score = 0.8972 * 100
percentile score ≈ 89.72
Therefore, if your body temperature is 99.00F, your percentile score would be approximately 89.72%. This means that approximately 89.72% of healthy adults have a body temperature lower than yours.