Assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of

9.6. If 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125

Z = (mean1 - mean2)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

0.9938

To find the probability that the mean blood pressure of 144 people will be less than 125, we can use the concept of the Central Limit Theorem. According to this theorem, when a large sample size is selected from a population, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution.

In this case, the distribution of blood pressure readings can be assumed to be normally distributed with a mean of 123 and a standard deviation of 9.6. Since the sample size is large (n = 144), we can use the normal distribution to approximate the distribution of the sample means.

First, we need to calculate the standard deviation of the sample means, also known as the standard error. The standard error (SE) is calculated by dividing the standard deviation of the population (σ) by the square root of the sample size (n).

SE = σ / √n
SE = 9.6 / √144
SE = 9.6 / 12
SE = 0.8

Next, we need to calculate the z-score, which measures the number of standard deviations a particular value is from the mean in a normal distribution. The z-score is calculated by subtracting the mean (μ) from the desired value (125) and then dividing by the standard error (SE).

z = (125 - 123) / 0.8
z = 2 / 0.8
z = 2.5

Now, we can use a standard normal distribution table or a calculator to find the probability associated with a z-score of 2.5.

Looking up the z-score of 2.5 in a standard normal distribution table, we find that the probability is approximately 0.9938.

Therefore, the probability that the mean blood pressure of 144 people will be less than 125 is approximately 0.9938.