Suppose we have a set of body temperature with a mean of 97.6 degrees and a standard deviation of 0.3 degrees. between what two values should 99% of all temperatures lie?
A cylindrical jelly jar is 5 inches across the top and about 10 inches high. How many cubic inches of jelly
could it hold (to the nearest hundredth)?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find Z score = the proportion .4950 between value and mean.
Z = (score-mean)/SD
Solve for the score values.
Remember that the Z score below the mean will be negative.
First, if you have a question, it is much better to put it in as a separate post in <Post a New Question> rather than attaching it to a previous question, where it is more likely to be overlooked.
V = π r^2 h
π = 3.14
r = diameter/2
To find the range of values within which 99% of the temperatures lie, we need to calculate the z-scores corresponding to the two percentiles: the lower bound and the upper bound.
First, we find the z-score corresponding to the lower bound of 99%. The z-score represents the number of standard deviations away from the mean.
Using the formula: z = (x - μ) / σ, where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For the lower bound, we want to find the z-score for the value below which 99% of the temperatures fall. This corresponds to the 0.5th percentile (1% divided by 2), which in a standard normal distribution is approximately -2.576.
Rearranging the formula, we can solve for the value x: x = z * σ + μ.
Plugging in the known values, we can calculate the lower bound:
Lower bound = -2.576 * 0.3 + 97.6
Next, we find the z-score corresponding to the upper bound of 99%, which is the 99.5th percentile. This value in a standard normal distribution is approximately 2.576.
Using the same rearranged formula, we can calculate the upper bound in a similar way:
Upper bound = 2.576 * 0.3 + 97.6
Therefore, between approximately 97.0 and 98.2 degrees should the temperatures fall within to cover 99% of all observations.