Answer:
Explanation:
To find the probability that the mean blood pressure of 32 randomly selected people will be less than 132, we need to use the central limit theorem. According to the central limit theorem, when the sample size is large enough, the distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
In this case, we are given that the blood pressure readings are normally distributed with a mean of 130 and a standard deviation of 4.6. Since we have a sample size of 32, which is considered large, we can use the normal distribution to approximate the distribution of the sample mean.
First, we need to calculate the standard error of the mean. The standard error of the mean is equal to the standard deviation divided by the square root of the sample size.
Standard error of the mean = 4.6 / √32 ≈ 0.812
Next, we need to standardize the value of 132 using the formula:
Z = (x - μ) / σ
Where Z is the z-score, x is the value we want to standardize (132), μ is the population mean (130), and σ is the population standard deviation (4.6).
Z = (132 - 130) / 0.812 ≈ 2.47
We can then find the probability associated with the z-score of 2.47 from the standard normal distribution table. Looking up the z-score of 2.47 in the table, we find that the corresponding probability is approximately 0.9930.
Therefore, the probability that the mean blood pressure of 32 randomly selected people will be less than 132 is approximately 0.9930. Hence, the correct answer is option A.