1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sveta_85 [38]
3 years ago
12

Diastolic blood pressure is a measure of the pressure when arteries rest between heartbeats. Suppose diastolic blood pressure le

vels in women are normally distributed with a mean of 69.3mm Hg and a standard deviation of 8.8mm Hg. Complete parts​ (a) and​ (b) below.
A. A diastolic blood pressure level above 90 mm Hg is considered to be hypertension. What percentage of women have​ hypertension?

B. If we randomly collect samples of women with 16 in each​ sample, what percentage of those samples have a mean above 90 mm​ Hg?
Mathematics
1 answer:
ddd [48]3 years ago
3 0

Answer:

a) P(X>90)=P(Z>\frac{90-69.3}{8.8})=P(Z>2.35)=1-P(Z

P(X>90)=1-\phi(2.35)=1-0.9906=0.0094

b) P(\bar X >90)=P(Z>\frac{90-69.3}{\frac{8.8}{\sqrt{16}}}=9.409)

And using a calculator, excel ir the normal standard table we have that:

P(Z>9.409)=1-P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

Let X the random variable that represent the blood pressure for women, and for this case we know the distribution for X is given by:

X \sim N(69.3,8.8)  

Where \mu=69.3 and \sigma=8.8

Part a

We are interested on this probability

P(X>90)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(X>90)=P(Z>\frac{90-69.3}{8.8})=P(Z>2.35)=1-P(Z

P(X>90)=1-\phi(2.35)=1-0.9906=0.0094

Part b

The distribution for the sample mean \bar X on this case is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we want to calculate the following probability:

P(\bar X >90)=P(Z>\frac{90-69.3}{\frac{8.8}{\sqrt{16}}}=9.409)

And using a calculator, excel ir the normal standard table we have that:

P(Z>9.409)=1-P(Z

You might be interested in
8minus 2n +3p has how many terms
Sunny_sXe [5.5K]

Answer:

It has two terms.

Step-by-step explanation:

4 0
2 years ago
Pls help i will mark brainlyest
Sergeeva-Olga [200]

Answer:

∠b=82°

Step-by-step explanation:

143°=∠c+∠b (exterior angle property)

143°=61°+∠b

∠b=143-61

∠b=82°

4 0
2 years ago
Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each mon
ICE Princess25 [194]
The answer is 16 days because 30/ 1.85 = 16 days
3 0
3 years ago
Let A and B be two disjoint events such that P(A) = 0.47 and P(B) = 0.3.<br><br> What is P(A or B)?
Alchen [17]
<h3>Answer:  0.77</h3>

Work Shown:

P(A or B) = P(A) + P(B)

P(A or B) = 0.47 + 0.30

P(A or B) = 0.77

Notes:

  • The formula only works if A and B are disjoint, aka mutually exclusive
  • If A and B are not disjoint, then use this formula: P(A or B) = P(A) + P(B) - P(A and B)
6 0
2 years ago
Read 2 more answers
(1×10,000)+(3×100)+(5×10)+(9× 10 1 ​ )+(8× 100 1 ​ ) as a decimal number.
andrey2020 [161]

Answer: 19,267.0


Step-by-step explanation:

1. You have the following information given in the problem above:

(1*10,000)+(3*100)+(5*10)+(9*101)+(8*1001)

2. To solve this exercise, first you must multiply the number that ar inside the parentheses and then you must add all of them, as you can see below:

10,000+300+50+909+8008=19,267

3. Rewriting is as a decimal, you have that the answer is:

19,267.0

8 0
2 years ago
Other questions:
  • A 300-page book is 10 inches long, 8 inches wide, and 3 4 inches tall. What is the volume of 100 pages of the book?
    14·2 answers
  • On the first day that tickets to the school play were sold, 100 tickets were sold for $230. Regular tickets cost $3 and student
    10·2 answers
  • What is the area of a trapezoid that has the following dimensions?
    15·2 answers
  • Explain the strategy you used to solve 287 divided into 41
    9·1 answer
  • zachary is planning to send a video game to each of his two brothers if he buys the same game for both brothers and pays $4.75 t
    7·2 answers
  • Which year had higher profits in month 5?
    13·2 answers
  • (1 point) Let f be a periodic function of period 10 such that f(x)=x2 for −5≤x&lt;5. Then the Fourier series of f is
    15·1 answer
  • Find the value of f(5).<br> y=f(x)
    11·1 answer
  • *PLEASE HELP QUICKLY!! 15 POINTS*
    7·2 answers
  • HELPPPPPPPPPP!!! pls show work
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!