Topic: Normal Probability Distribution
Question: Assume that blood pressure readings are normally distributed with a mean if 116 and a standard deviation of 4.8. If the 36 people are randomly selected, How do I find the probability that their blood pressure will be less than 118?
http://davidmlane.com/hyperstat/z_table.html
To find the probability that the blood pressure of the 36 randomly selected people will be less than 118, you can use the concept of the normal probability distribution and the standard normal distribution.
Here are the steps to calculate this probability:
Step 1: Standardize the value
To use the standard normal distribution, we need to convert the given values to z-scores. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x = the value we want to standardize (in this case, 118)
μ = the mean of the distribution (116)
σ = the standard deviation of the distribution (4.8)
So, plugging in the values, the z-score is:
z = (118 - 116) / 4.8
Step 2: Look up the z-score
Once you have the z-score, you can find the corresponding probability in the standard normal distribution table. This table gives you the area under the curve to the left of a given z-score.
For example, if the z-score is 0.50, the table might say that the area to the left of that z-score is 0.6915.
Step 3: Interpret the result
The probability that the blood pressure of the 36 randomly selected people will be less than 118 is the area under the curve to the left of the z-score you calculated in Step 1.
Remember that the z-score represents the number of standard deviations from the mean. In this case, it tells you how many standard deviations above or below the mean the value of 118 is.
By following these steps, you can find the probability that the blood pressure will be less than 118.