STATS HELP PLEASE

Question

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.

Round the probabilities to four decimal places.

It is possible with rounding for a probability to be 0.0000.

a) State the random variable.

orrect

b) Find the probability that a randomly selected person in China has a blood pressure of 148.7 mmHg or more.

   Incorrect

c) Find the probability that a randomly selected person in China has a blood pressure of 155.3 mmHg or less.

   Incorrect

d) Find the probability that a randomly selected person in China has a blood pressure between 148.7 and 155.3 mmHg.

   Incorrect

e) Find the probability that randomly selected person in China has a blood pressure that is at most 70.5 mmHg.

   Correct

f) Is a blood pressure of 70.5 mmHg unusually low for a randomly selected person in China?

  Why or why not?

  

g) What blood pressure do 58% of all people in China have less than?

  Round your answer to two decimal places in the first box.

  Put the correct units in the second box.

Answer 1

To answer these probability questions regarding blood pressure in China, we'll use the standard normal distribution since the data is assumed to be normally distributed. Z-scores will help us calculate probabilities.

a) Random variable: Blood pressure (in mmHg)

b) Find the probability that a randomly selected person in China has a blood pressure of 148.7 mmHg or more.

You'll need to find the z-score for 148.7 mmHg using the formula:

\[Z = \frac{(X - \mu)}{\sigma}\]

Where X is the value (148.7 mmHg), μ is the mean (128 mmHg), and σ is the standard deviation (23 mmHg).

Once you find the Z-score, use a standard normal distribution table (or calculator) to find the probability that Z is greater than or equal to this Z-score.

c) Find the probability that a randomly selected person in China has a blood pressure of 155.3 mmHg or less.

Use the same formula to find the Z-score for 155.3 mmHg, then use the standard normal distribution table to find the probability that Z is less than or equal to this Z-score.

d) Find the probability that a randomly selected person in China has a blood pressure between 148.7 and 155.3 mmHg.

Calculate the Z-scores for both values (148.7 and 155.3 mmHg) and find the probabilities for each. Subtract the probability for 148.7 mmHg or less from the probability for 155.3 mmHg or less to find the probability within this range.

e) Find the probability that a randomly selected person in China has a blood pressure that is at most 70.5 mmHg.

Calculate the Z-score for 70.5 mmHg, then use the standard normal distribution table to find the probability that Z is less than or equal to this Z-score.

f) Whether 70.5 mmHg is unusually low or not depends on the context and medical standards. You would need information about the typical range of blood pressure values in China and medical guidelines to determine if it's unusually low.

g) To find the blood pressure value below which 58% of all people in China fall, you need to find the Z-score that corresponds to the 58th percentile (0.58 probability). You can then use this Z-score to calculate the corresponding blood pressure value.

Remember to round your answers as requested and use the standard normal distribution table or calculator for Z-score to probability conversions.