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Chapter 2: Q 56. (page 140)

Blood pressure According to a health information website, the distribution of adults鈥� diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70and a standard deviation 20A diastolic pressure above 100Around 6.68% of the adults have very high blood pressure according to the criterion. for an adult is classified as very high blood pressure. About what proportion of adults have very high blood pressure according to this criterion?

Short Answer

Expert verified

Around 6.68% of the adults have very high blood pressure according to the criterion.

Step by step solution

01

Given information

Diastolic pressure value,x=100

Mean,渭=70

Standard deviation,蟽=20

02

Concept

The formula used:z=x鈭�渭蟽

03

Calculation

Calculate the Z鈭�score,

z=x鈭�渭蟽=100鈭�7020=1.50

To find the equivalent probability, use the normal probability table in the appendix.

The usual normal probability table for P(z<0.80) has a row that starts with 1.5 and a column that starts with.00

P(x>100)=P(z<1.50)=1鈭�P(z>0.80)=1鈭�0.9332=0.0668=6.68%

Therefore,

Around 6.68percent of persons have a diastolic pressure greater than100 which is considered extremely high blood pressure.

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Most popular questions from this chapter

Long jump Refer to Exercise 21 Suppose that the corrected long-jump

distances are converted from centimeters to meters (note that 100cm=1m ).

a. What shape would the resulting distribution have? Explain your answer.

b. Find the mean of the distribution of corrected long-jump distance in meters.

c. Find the standard deviation of the distribution of corrected long-jump distance in meters.

Flight times An airline flies the same route at the same time each day. The flight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the flight takes more than an hour. On 3% of days, the flight lasts 75 minutes or more. Use this information to determine the mean and standard deviation of the flight time distribution.

Big sharks Here are the lengths (in feet) of 44 great white sharks:

A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68鈥�95鈥�99.7 rule.

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44155862.559.413.5515.7517.222.8

Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.

a. z>鈭�1.66

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Put a lid on it! Refer to Exercise 56. The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to less than 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.

(a) If the standard deviation remains at 蟽=0.02inches, at what value should the supplier set the mean diameter of its large-cup lids to ensure that less than 1%are too small to fit? Show your method.

(b) If the mean diameter stays at 渭=3.98inches, what value of the standard deviation will result in less than 1%of lids that are too small to fit? Show your method.

(c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)
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