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
Paul [167]
3 years ago
8

A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribut

ion is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Mathematics
1 answer:
creativ13 [48]3 years ago
6 0

Answer:

Explained below.

Step-by-step explanation:

Let <em>X</em> = systolic blood pressure measurements.

It is provided that, X\sim N(\mu=80,\sigma^{2}=3^{2}).

(a)

Compute the percentage of measurements that are between 71 and 89 as follows:

P(71

                        =P(-3

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of measurements that are between 71 and 89 is 99.73%.

(b)

Compute the probability that a person's blood systolic pressure measures more than 89 as follows:

P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})

                =P(Z>3)\\=1-P(Z

Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.

(c)

Compute the probability that a person's blood systolic pressure being at most 75 as follows:

Apply continuity correction:

P(X\leq 75)=P(X

                =P(X

Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.

(d)

Let <em>x</em> be the blood pressure required.

Then,

P (X < x) = 0.15

⇒ P (Z < z) = 0.15

⇒ <em>z</em> = -1.04

Compute the value of <em>x</em> as follows:

z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9

Thus, the 15% of patients are expected to have a blood pressure below 76.9.

(e)

A <em>z</em>-score more than 2 or less than -2 are considered as unusual.

Compute the <em>z</em> score for \bar x as follows:

z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}

  =\frac{84-80}{3/\sqrt{3}}\\\\=2.31

The <em>z</em>-score for the mean blood pressure measurement of 3 patients is more than 2.

Thus, it would be unusual.

You might be interested in
(11x – 6x2 – 8)/(3x – 1)
kozerog [31]

Answer:

46.6

Step-by-step explanation:

have a good day

6 0
3 years ago
NEED HELP NOW 25 POINTS 5 PHOTOS WILL MARK BRAINLIEST ANSWER!!! HURRY!!!!!!
Andru [333]
The function to the graph is 6
4 0
3 years ago
What is (6,2) rotation 270
nignag [31]

Given:

The point is (6,2).

To find:

The image of given point after rotation of 270 degrees.

Solution:

Let the given point be P(6,2).

Rotation of 270 degrees means the figure is rotated 270 degrees counterclockwise about the origin. So, the rule of rotation is

(x,y)\to (y,-x)

Using this rule, we get

P(6,2)\to P'(2,-6)

Therefore, the image of given point is (2,-6).

3 0
3 years ago
2y to the 2nd power +11y +14
goldfiish [28.3K]

2y^2 +11y+14 =(2y+7)(y+2)

Step-by-step explanation:

Given

2y^2 +11y+14

=2y^2 +(7+4)y+14

=2y^2+7y+4y+14

= y(2y+7) + 2(2y+7)

=(2y+7)(y+2)

3 0
3 years ago
Can you use division to solve a missing factor problem
klasskru [66]
Yes, you can use division to solve a missing factor problem
5 0
3 years ago
Other questions:
  • Maya has 120 caramel apples to sell. Each caramel apple is covered with one topping.
    13·1 answer
  • A line with a slope of 1/8 passes through the points (u, -9) and (6, -8). what is the value of u?
    5·1 answer
  • 7(h+3)=6(h-3) pls help
    10·1 answer
  • A garden has a length of 9 1/6<br> feet and a width of 6 3/4<br> feet. what is the area
    13·1 answer
  • Which expression has the same value as the sum of 45 and 25?
    8·1 answer
  • I’m new to this app and I need help with those two questions please help!!
    6·1 answer
  • Are the lines perpendicular? x = 3 and y = 5 *
    5·1 answer
  • Which quadratic equation has roots –2 and 1/5?
    8·1 answer
  • Furaha sold a mobile phone at sh.6000 making a profit of 20%. what was the buying price????​
    7·1 answer
  • A boat can travel 120 kilometers on 60 liters of gas. How far can it travel on 197 liters
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!