Jim's systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim's age group, 140 is the cutoff for high blood pressure.



If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be, (Round your answers to 4 decimal places.)

(a) 135 or less?
(b) 175 or more?
(c) between 125 and 165?

Statistics show that the sales force of a certain company successfully closed 468 sales out of 900 sales calls. What was their percent success rate?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.

First, if you have a question, it is much better to put it in as a separate post in <Post a New Question> rather than attaching it to a previous question, where it is more likely to be overlooked.

468/900 * 100 = ?

To find the probability in each case, we need to use the concept of the standard normal distribution. We can convert Jim's systolic blood pressure data to a standard normal distribution using z-scores.

(a) To find the probability that Jim's systolic blood pressure is 135 or less, we need to find the z-score for 135 first. The z-score formula is given by:

z = (X - μ) / σ

where X is the observed value, μ is the mean, and σ is the standard deviation.

For 135, the z-score is:

z = (135 - 145) / 20 = -0.5

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of -0.5. The probability is the area under the curve to the left of the z-score.

P(135 or less) = P(z ≤ -0.5)

Using a standard normal distribution table, we find that P(z ≤ -0.5) is approximately 0.3085.

Therefore, the probability that Jim's systolic blood pressure is 135 or less is approximately 0.3085.

(b) To find the probability that Jim's systolic blood pressure is 175 or more, we need to find the z-score for 175. The z-score formula is the same as before:

z = (X - μ) / σ

For 175, the z-score is:

z = (175 - 145) / 20 = 1.5

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of 1.5. The probability is the area under the curve to the right of the z-score.

P(175 or more) = P(z ≥ 1.5)

Using a standard normal distribution table, we find that P(z ≥ 1.5) is approximately 0.0668.

Therefore, the probability that Jim's systolic blood pressure is 175 or more is approximately 0.0668.

(c) To find the probability that Jim's systolic blood pressure is between 125 and 165, we can find the probabilities for both individual values and then subtract them.

Using the z-score formula:

For 125, the z-score is:

z = (125 - 145) / 20 = -1

For 165, the z-score is:

z = (165 - 145) / 20 = 1

Using a standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-scores.

P(125≤ X ≤165) = P(-1 ≤ z ≤ 1)

Using a standard normal distribution table, we find that P(-1 ≤ z ≤ 1) is approximately 0.6826.

Therefore, the probability that Jim's systolic blood pressure is between 125 and 165 is approximately 0.6826.