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Chapter 6: Q.6.64 (page 389)

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean 碌=125and standard deviation 蟽=14. Systolic blood pressure for males follows a normal distribution.

a. Calculate the z-scores for the male systolic blood pressures 100and 150millimeters.

b. If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 150 millimeters, what would you say to him?

Short Answer

Expert verified
  1. The z-score of the systolic blood pressures 100is -1.79and 150is 1.79.
  2. The given z-score is more than the given range 100 and 150 so, the friends believe is wrong.

Step by step solution

01

Given information (Part a)

Given in the question that

Mean=125

Standard deviation=14

X~N(125,14)

02

Solution (Part a)

Here we need to calculate the z-score for 100

z=x鈭�渭蟽

=100鈭�12514

=鈭�1.79

Again we need to calculate the z-score of 150

z=x鈭�渭蟽

=150鈭�12514

=1.79

03

Given information (Part b)

Given in the question that

Mean =125

Standard deviation =14

X~N(125,14)

04

Solution (Part b)

Here the z-score has been given as 2.5and we need to find the blood pressure,

z=x鈭�渭蟽

2.5=x鈭�12514

x=2.5脳14+125

=160

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Most popular questions from this chapter

Kyle鈥檚 doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean 碌=125and standard deviation 蟽=14. If X = a systolic blood pressure score then X~N(125,14).

a. Which answer(s) is/are correct?

  1. Kyle鈥檚 systolic blood pressure is 175.
  2. Kyle鈥檚 systolic blood pressure is 1.75times the average blood pressure of men his age.
  3. Kyle鈥檚 systolic blood pressure is 1.75above the average systolic blood pressure of men his age. i
  4. Kyles鈥檚 systolic blood pressure is1.75 standard deviations above the average systolic blood pressure for men.

b. Calculate Kyle鈥檚 blood pressure.

In 2005,1,475,623students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean 碌=520and standard deviation 蟽=115

  1. Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence.
  2. What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score?
  3. For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the test they took?

A company manufactures rubber balls. The mean diameter of a ball is 12cmwith a standard deviation of 0.2 cm. Define the random variable Xin words. X=______________.

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

a. If X = distance in feet for a fly ball, then X ~ _____(_____,_____)

b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

齿词狈(鈥�4,1)

What is the median?
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