A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean = 87 and standard deviation = 25. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60



(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 125 (borderline diabetes starts at 125)

Answers

Answer 1

Using the normal distribution, it is found that:

a) 0.8599 = 85.99% probability that x is more than 60.

b) 0.1788 = 17.88% probability that x is less than 110.

c) 0.6811 = 68.11% probability that x is between 60 and 110.

d) 0.0643 = 6.43% probability that x is greater than 125.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of 87, thus [tex]\mu = 87[/tex].The standard deviation is of 25, thus [tex]\sigma = 25[/tex].

Item a:

This probability is 1 subtracted by the p-value of Z when X = 60, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60 - 87}{25}[/tex]

[tex]Z = -1.08[/tex]

[tex]Z = -1.08[/tex] has a p-value of 0.1401.

1 - 0.1401 = 0.8599

0.8599 = 85.99% probability that x is more than 60.

Item b:

This probability is the p-value of Z when X = 110, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 87}{25}[/tex]

[tex]Z = 0.92[/tex]

[tex]Z = 0.92[/tex] has a p-value of 0.8212.

1 - 0.8212 = 0.1788.

0.1788 = 17.88% probability that x is less than 110.

Item c:

This probability is the p-value of Z when X = 110 subtracted by the p-value of Z when X = 60.

From the previous two items, 0.8212 - 0.1401 = 0.6811.

0.6811 = 68.11% probability that x is between 60 and 110.

Item d:

This probability is 1 subtracted by the p-value of Z when X = 125, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{125 - 87}{25}[/tex]

[tex]Z = 1.52[/tex]

[tex]Z = 1.52[/tex] has a p-value of 0.9357.

1 - 0.9357 = 0.0643.

0.0643 = 6.43% probability that x is greater than 125.

A similar problem is given at https://brainly.com/question/24863330


Related Questions

Justin recently drove to visit his parents who live 96 miles away. On his way there his average speed was 20 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 4 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.

Justin's average speed to his parents' house: __________ mph

Justin's average speed from his parents' house: __________ mph

Answers

Answer:

Justin's average speed to his parents' house: x= 40mph

Justin's average speed from his parents' house: x+20=60 mph

Step-by-step explanation:

Let the average speed be x +20  

Then average speed from his parents' x

And the distance is S=96

Then we know :

[tex]\displaystyle \frac{S}{x+20} +\frac{S}{x} =4 \\\\\\ \frac{96}{x+20} +\frac{96}{x}=4 \ |\div 4 \\\\\\ 24\bigg(\frac{1}{x+20} +\frac{1}{x} \bigg) =1 \\\\\\ 24\cdot \frac{x+x+20}{(x+20)x} =1 \ |\cdot (x+20)x \ \ \\\\\\48x+480=x^2+20x \\\\ x^2-28x-480=0 \\\\ \rm D=28^2+4\cdot 480=2704 =52^2 \\\\ \boxed{x_1=\frac{28+52}{2} =40} \\\\x_2=\frac{28-52}{2} =-12 \ \ \varnothing[/tex]

Justin's average speed to his parents' house:  x= 40mph

Justin's average speed from his parents' house:  x+20=60 mph

each runner in a 4 4/5 mile relay race runs 4/5 of a mile.find the number of runners on a relay team

Answers

Answer:

Divide total distance of the race by the length each runner runs:

Divide total distance of the race by the length each runner runs:8 miles / 4/5

Divide total distance of the race by the length each runner runs:8 miles / 4/5When dividing by a fraction flip the fraction over and multiply:

Divide total distance of the race by the length each runner runs:8 miles / 4/5When dividing by a fraction flip the fraction over and multiply:8 miles x 5/4 = (8×5)/4 = 40/4 = 10

Divide total distance of the race by the length each runner runs:8 miles / 4/5When dividing by a fraction flip the fraction over and multiply:8 miles x 5/4 = (8×5)/4 = 40/4 = 10There are 10 runners

Step-by-step explanation:

HOPE IT HELPS YOU

Answer:

6 runners

Step-by-step explanation:

4 4/5 divided by 4/5 is 6.

Ken took 64 minutes to walk 4 miles on flat terrain. If he walked at a constant rate, how long would it take Ken to complete 5 miles?

Answers

Answer: 80 minutes

Step-by-step explanation:in the picture

SOLVE ASAP!!!!! NO LINKS!!!!!!∛²³1 + 4 x -96

Answers

Answer:

All i got was 3√23+4x−96

Step-by-step explanation:

Assume that y varies inversely as x. If
Y
y = 10 when
=
x = 4, what is the value for y when
x = 6?

Answers

Answer:

x=5

Explanation:

y∝1x∴y=k⋅1x∴x⋅y=k;

When x=4;y=10∴4⋅10=kork=40.

So variation equation is x⋅y=40

When y=8;x=408=5∴x=5 [Ans]

Step-by-step explanation:

not surre

Answer:

6.67

Step-by-step explanation:

10=4

y=6

10×4/6

Quickly answer number 10 text only no fonts (100 points) mark brainliest

Answers

25

have a great day! :3

Answer:

Hello again the square root of 625 is 25

A square field is 30 m long.Find the length of wire required to fence it with 4 rounds​

Answers

Answer:

120m

Step-by-step explanation:

because 30×4 is 120

what is the expanded form of 203,574

Answers

Expanded Notation Form:

 203,574 =

 200,000  

+ 0  

+ 3,000  

+ 500  

+ 70  

+ 4  

Expanded Factors Form:

   203,574 =

 2 × 100,000  

+ 0 × 10,000  

+ 3 × 1,000  

+ 5 × 100  

+ 7 × 10  

+ 4 × 1  

Expanded Exponential Form:

 203,574 =

2 × 105

+ 0 × 104

+ 3 × 103

+ 5 × 102

+ 7 × 101

+ 4 × 100

200000+0+3000+500+70+4

Can someone pls help me I really need help in here.. PLS…
And if u can explain how you make it I will appreciate it,. Thank u:(((

Answers

Answer:

So, "Compare the following rational numbers," its asking which of them is greater, or if there equal to each other.

So for 3.25 and 3 1/2

3 1/2 is greater

3.25 < 3 1/2 (so it should look like this when the symbol on that side)

and for -4.5 and -4.05

-4.05 is greater.

-4.5 < -4.05  (so the symbol is also on that side.)

add 3 3/5 + 6 3/10 tyyyyy

Answers

[tex] = 9 \frac{9}{10} \\ \\ in \: \: alternate \: \: forms \\ \\ \frac{99}{10} \: \: \: and \: \: 9.9 \\ \\ hope \: it \: \: helps[/tex]

see the attachment!

Help or don’t if so thank you

Answers

Answer: 12.60 per CD

Step-by-step explanation:

Tax 0.80 * 3 = 2.40

40.20 - 2.40 = 37.80

37.8 / 3 = 12.60








What is the value of the expression 30-(-6)?
-180
-5
Ο Ο Ο Ο
5
24

Answers

Answer:30-(-6) is the same as 30+6. 36 is the value of the expression 30-(-6). If it were written:

30x(-6) = -180

30-6 = 24

But 30-(-6) = 36

Step-by-step explanation:

Fractions
9/4 = ?/28 can u help me solve this explination please

Answers

The answer is 63. The denominators are 7. Times the numerator by 7 and you’ll get 63

I just need mental help at this point​

Answers

Answer:

1:2

Step-by-step explanation:

QRS is double the size of TUV

Helpp need it now


9.) Find the N' .

1.) {j , u , d , g}
2.) {m , n , t , a , l}
3.) {j , u , d , g , e}
4.) {m , e , n , t , a , l}

10.) Find the N U I.

1.) {m , n , t , a , l}
2.) {j , u , d , g , e}
3.) {m , e , n , t , a , l}
4.) {j , u , d , g , m , e , n , t , a , l}

Answers

Answer:

8.) ans {e}

9.) ans {j, u, d, g}

10.) ans {j, u, d, g, m, e, n, t, a, l}

Find x. Round your answer to the nearest tenth of a degree.

Answers

Answer:

x = 50.5°

Step-by-step explanation:

Use SOH CAH TOA... Since the adjacent and hypotenuse are given, you must use cosine.

cos(x) = 14/22

cos^-1 (14/22) = 50.5°

Hello, i need some help for questions 2-5 please

Answers

Answers:

4. =9.999........

Examplantion :

5×2÷3=9.99999..........

7.
Write an equation in point-slope form for the line through the given point with the given slope.

(10, –9); m = –2

A. y – 10 = –2(x + 9)

B. y – 9 = –2(x – 10)

C. y – 9 = –2(x + 10)

D. y + 9 = –2(x – 10)

Answers

Answer:

D. y + 9 = –2(x – 10)

Step-by-step explanation:

GradPoint answer

I also got the answer correct on the quiz.

Your mother drives 60 minutes at a constant speed of 40 miles per hour. She then speeds up, and drives for another 30 minutes at a constant speed of 70 miles per hour. How many miles does your mother travel all together? How long did the trip take?

Answers

Answer: written below

Step-by-step explanation:

1 hour time 40 miles/ hour =1*40=40miles

0.5 *70=0.5*70=35 miles

40+35=75 miles

60 minutes+30 minutes= 90 minutes or 1 1/2hours

Need help with number 31

Answers

Answer:

Kelly's wrong, because 97/1000 can be written as 0.097 not 0.97.

Step-by-step explanation:

you would get 0.97 by dividing 97 by 100.

can anyone heelp me pls

Answers

Lotion - liquid

Suspension- semisolid

Capsule- Solid

Hope this helps :)

Triangles PQR and XYZ are similar. What is the length of XZ?

Answers

3x3x3x3x3= you do the math

Write the expression in rational exponent form.[tex](\sqrt[4]{x}+5)^{3}[/tex]

Answers

[tex] = \: \: \: \sqrt[4]{ {x}^{3} + 15 \sqrt{x} + 75 \sqrt[4]{x} + 125 } [/tex]

hope it helps

see the attachment

I NEED A 100% ACCURATE ANSWER FOR THIS ASAP NO LINKS !!!
Solve the following: 7y−20=3y+12
1: y= 3.2
2: y=8
2: y= -8
4: y= 28

Answers

Answer:

y=8

Step-by-step explanation:

7y-20=3y+12

7y-3y=12+20

4y/4=32/4

y=8

Answer:

7y-3y=12+20

4y=32

y=8

that's it. i don't know why I need 20 max character to submit

the general solution of sinx + cosx =√2 is..??​

Answers

The answer is A. x= [tex]\pi[/tex]/4 +2[tex]\pi[/tex]n

Answer:

the general solution has answer

2nπ+π/4

If you want someone to do your homework assignments for you (math, English) for a cheap price lmk

Answers

Answer:

I do lol

Step-by-step explanation:

Answer:

why would you wanna do someone's homework on Math and English?

Step-by-step explanation:

they wouldn't learn anything if they make you do their homework, besides what's the point of the homework if they don't learn anything? I know homework's are hard, but they give it for you to understand more of the lesson.

and you will also make yourself tired doing someone's homework what about your responsibilities?

It'll be only beneficial for you but not for them yeah you'll get money but its best if you let them do their homework. I mean homework's aren't that bad.

They just think they can't do it cause their lazy, and they think they wouldn't know the answer. Besides they can't just lay around all day because they paid you for doing their homework, they won't even know if your scamming them.

William has a lemonade stand. Today he made $89.62 in lemonade sales and one third that amount in cookie sales. How much money did William make altogether?

Answers

Answer:

$119.49 (rounded to the nearest cent.)

Answer: 119.4933333 would be the actual answer but rounded to the nearest cent it would be 119.49

89.62/3 = 29.8733333....... 89.62 + 29.8733333 = 119.4933333

I have no idea how to draw the last one … any help plz

Answers

Answer:

The intersection of the x and y axis is one point one the line, another one is (1, 1). The range of y<x is below the line I just described.

Step-by-step explanation:

what 21.807-10.739=?​

Answers

Answer:

2.428 is the answer....

Which graph represents the function f(x)=4⋅3x?

Answers

Answer: Bottom right corner (southwest corner)

Explanation:

Plug in x = 0 to find that

[tex]f(x) = 4*3^x\\\\f(0) = 4*3^0\\\\f(0) = 4*1\\\\f(0) = 4\\\\[/tex]

This shows that the y intercept is (0,4).

Of the four answer choices, only the bottom right corner has this y intercept. Note that the curve goes uphill when moving to the right. This function is increasing which matches with f(x) being an increasing function. In other words, f(x) represents exponential growth.

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