suppose you have a set of blood pressures with a mean of 80 diastolic, and standard deviation of 5 points. assuming a normal distribution of blood pressures what two values should 95% of all blood pressures lie? please show all calculations. thank you very much
see the other post.
what other post, i don't know what you mean. can you show me the calculations? i have no idea where to begin and getting very frustrated. thank you very much.
mary
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score = proportion of .475 from the mean. Insert Z value (one positive and one negative) and solve for your score values.
To find the two values within which 95% of all blood pressures lie, we will use the Z-score formula and the properties of the normal distribution.
1. Z-score formula: The Z-score of any observation in a normal distribution can be calculated using the formula:
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the individual observation
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
2. Z-score for 95% of the data: Since we want to find the range that includes 95% of the data, we can find the corresponding Z-score using a standard normal distribution table or a Z-score calculator. For a 95% confidence level, the corresponding Z-score is approximately 1.96.
3. Calculating the range:
- To find the upper bound, we'll use the formula:
X = μ + (Z * σ)
X = 80 + (1.96 * 5)
X ≈ 80 + 9.8
X ≈ 89.8
- To find the lower bound, we'll use the formula:
X = μ - (Z * σ)
X = 80 - (1.96 * 5)
X ≈ 80 - 9.8
X ≈ 70.2
Therefore, with a mean of 80 and a standard deviation of 5, 95% of all blood pressures lie between approximately 70.2 and 89.8 diastolic.