Question

assume that blood pressure readings are normallh distributed with a mean of 113 and standard deviation of 4.8 if 36 people are selected. find the probability that their mean blood pressure will be less than 117

Answer 1

Answer 2

To find the probability that the mean blood pressure of 36 people will be less than 117, we can use the Central Limit Theorem. According to the Central Limit Theorem, when a sample size is sufficiently large (such as in this case with 36 people), the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution.

The mean of the sample means will be equal to the population mean, which is 113 in this case. The standard deviation of the sample means, also known as the standard error of the mean, can be calculated by dividing the population standard deviation by the square root of the sample size. Thus:

Standard error of the mean (SE) = standard deviation / sqrt(sample size) SE = 4.8 / sqrt(36) = 4.8 / 6 = 0.8

Now, we need to find the z-score, which is a measure of how many standard deviations an observation or sample mean is away from the population mean. We can use the z-score formula:

z = (sample mean - population mean) / SE

z = (117 - 113) / 0.8 = 5 / 0.8 = 6.25

To find the probability of a z-score less than 6.25, we consult a standard normal distribution table or use a calculator. The probability associated with a z-score of 6.25 is essentially 1 because it is extremely rare for a value to be more than 6 standard deviations away from the mean in a normal distribution.

Therefore, the probability that the mean blood pressure of 36 people will be less than 117 is nearly 1 (or 100%).