Question

1. **I.** Engineers must consider the breadths of
male heads when designing helmets. The company researchers have
determined that the population of potential clientele have head
breadths that are normally distributed with a mean of 6.8-in and a
standard deviation of 0.8-in. Due to financial constraints, the
helmets will be designed to fit all men except those with head
breadths that are in the smallest 2.6% or largest 2.6%.

What is the minimum head breadth that will fit the clientele?

min = inches

What is the maximum head breadth that will fit the clientele?

min = inches

Enter your answer as a number accurate to 1 decimal place. Answers
obtained using exact *z*-scores or *z*-scores rounded
to 3 decimal places are accepted.

**II.** The systolic blood pressure of adults in a
large city is nearly normally distributed with a mean of 117 and
standard deviation of 23 .

Someone qualifies as having Stage 2 high blood pressure if their
systolic blood pressure is 160 or higher.

a. Around what percentage of adults in the USA have stage 2 high
blood pressure? Give your answer rounded to two decimal
places.

%

b. If you sampled 2000 people, how many would you expect to have
BP> 160? Give your answer to the nearest person.

people

c. Stage 1 high BP is specified as systolic BP between 140 and 160.
What percentage of adults in the US qualify for stage 1?

%

d. Your doctor tells you you are in the 30th percentile for blood
pressure among US adults. What is your systolic BP? Round to 2
decimal places.

lbs

Answer #1

Let X denote the head breadth.

a)P(X<x)=0.026 which implies x=5.2 inch

b)P(X>x)=0.026 which iplies x=8.4 inch

Let Y denote systolic blood pressure.

a)percentage of people have stage 2 systolic BP=100*0.03077211=3.08% approximately

b)number of people havinh=g stage 2 BP among 2000 peolple=2000*0.03077211=62 approximately

c)percentage of adults have stage 1 systolic BP=100*0.1278831=12.79% approximately

d)30th percentile of the distribution=104.94

**R CODE:**

**> 6.8+0.8*qnorm(.026)
[1] 5.245493
> 6.8+0.8*qnorm(.026,lower.tail=FALSE)
[1] 8.354507
>
>
> pnorm(160,117,23,lower.tail=FALSE)
[1] 0.03077211**

**> 2000*0.03077211
[1] 61.54422
>
pnorm(160,117,23,lower.tail=TRUE)-pnorm(140,117,23,lower.tail=TRUE)
[1] 0.1278831
> qnorm(0.30,117,23)
[1] 104.9388**

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.2-in and a standard deviation
of 1.1-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 2.6% or largest 2.6%. What is the minimum head breadth
that will fit the clientele? min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.2-in and a standard deviation
of 1.1-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 3.5% or largest 3.5%. What is the minimum head breadth
that will fit the clientele? min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 5.8-in and a standard deviation
of 1-in. Due to financial constraints, the helmets will be designed
to fit all men except those with head breadths that are in the
smallest 0.9% or largest 0.9%.
What is the minimum head breadth that will fit the clientele?
min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.6-in and a standard deviation
of 1-in. Due to financial constraints, the helmets will be designed
to fit all men except those with head breadths that are in the
smallest 2.1% or largest 2.1%. What is the minimum head breadth
that will fit the clientele? min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.4-in and a standard deviation
of 0.9-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 1.1% or largest 1.1%. What is the minimum head breadth
that will fit the clientele? min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.8-in and a standard deviation
of 0.8-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 3% or largest 3%.
What is the minimum head breadth that will fit the clientele?
min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 7.1-in and a standard deviation
of 1-in. Due to financial constraints, the helmets will be designed
to fit all men except those with head breadths that are in the
smallest 4.5% or largest 4.5%. What is the minimum head breadth
that will fit the clientele?
min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.3-in and a standard deviation
of 1-in. Due to financial constraints, the helmets will be designed
to fit all men except those with head breadths that are in the
smallest 1.3% or largest 1.3%. What is the minimum head breadth
that will fit the clientele? min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 5.6-in and a standard deviation
of 1.1-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 3.2% or largest 3.2%.
What is the minimum head breadth that will fit the clientele?
min =...

Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 6.3-in and a standard deviation
of 1-in. Due to financial constraints, the helmets will be designed
to fit all men except those with head breadths that are in the
smallest 2.1% or largest 2.1%.
What is the minimum head breadth that will fit the
clientele?
(round your...

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