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
Gala2k [10]
3 years ago
12

Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a

nd standard deviation of 16 day
a. What is the probability that the sample mean length of pregnancy for 15 randomly selected women lasts less than 260 days.
b. The probability that the total length of pregnancy for 15 randomly selected women is greater than a certain amount is 0.05. Find this total length.
c. What is the probability that the sample total length of pregnancy for 7 randomly selected women is between 1800 and 1900 days?
d. The probability that the average length of pregnancy for randomly selected women is greater than 270 is 0.1151. Find the sample size of the random sample.
Mathematics
1 answer:
Kaylis [27]3 years ago
6 0

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }

Z*(Sigma/\sqrt{n} )= (X[bar]-Mu)

(Sigma/\sqrt{n} )= \frac{(X[bar]-Mu)}{Z}

Sigma= \frac{(X[bar]-Mu)}{Z}*\sqrt{n}

Sigma*(\frac{Z}{(X[bar]-Mu)})= \sqrt{n}

n = (Sigma*(\frac{Z}{(X[bar]-Mu)}))^2

n = (16*(\frac{1.2}{(270-264)}))^2

n= 10.24 ≅ 11 pregnant women.

I hope it helps!

You might be interested in
a man paid $8000 for a car since then ,its value has fallen by 25% calculate the current value please help me​
Anna [14]

Answer:

$6000

Step-by-step explanation:

so basically, 25% of the 100% value is gone, right? which means that 75% of the value would remain. After that, all is easy. 8000*0.75, since 75% is 0.75, and the answer of that is 6000, so the current value is 6000 dollars.

3 0
2 years ago
What is the sum of 3/5 and 1/10?
Blababa [14]
The sum of 3/5 and 1/10 is 7/10.
6 0
3 years ago
I do not know this answer
nexus9112 [7]
The answer is (3, -5)
3 0
2 years ago
Read 2 more answers
Xavier Martinez took out a $5,000 loan at 7.5% interest for reconstructing his patio. His monthly payment on the 12-month loan w
Norma-Jean [14]
Paying off the entire loan = 12 * 437.26 = <span> <span> <span> 5,247.12 </span> </span> </span>
He paid 6 * 437.26 = <span> <span> <span> 2,623.56 </span> </span> </span>
He then paid 2,556.03

2,623.56  plus = 2,556.03 = <span> <span> <span> 5,179.59 </span> </span> </span>

<span> <span> 5,247.12 </span> minus </span><span>5,179.59 =
67.53 the amount of money he saved.

</span>
3 0
3 years ago
Read 2 more answers
F(x)=|3x+5|+6<br> g(x)=7<br> find (f+g) (x).
horrorfan [7]

Answer:

(f+g) (x)=\mid 3x+5\mid+13

Step-by-step explanation:

<u>Operation of Functions</u>

Given:

f(x)=\mid 3x+5\mid+6

g(x)=7

The sum of (f+g) (x) is:

(f+g) (x)=\mid 3x+5\mid+6+7

We cannot operate with the expression inside the absolute bars, thus:

\boxed{(f+g) (x)=\mid 3x+5\mid+13}

8 0
3 years ago
Other questions:
  • Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same
    7·1 answer
  • Assessment 2 Solving Equations (w. Distribution). -7(-x + 8) + 2x = -5 - 8x show your work pleaes
    10·2 answers
  • Sophia is making brownies. Her recipe uses a ratio of 3 cups of sugar to 2 cups of cocoa powder.
    12·1 answer
  • A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue)
    15·1 answer
  • The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is 1/18. Use this inf
    14·1 answer
  • PLEASE HELP EVERYONE KEEPS TROLLING PLEASE DONT TROLL
    6·1 answer
  • If you have 70 red blocks and 84 green blocks, what is the greatest number of identical block stacks that can be made without an
    5·1 answer
  • Find - 5+(-3) + 5.
    15·1 answer
  • The following playing cards are used in a game. What is the probability of not selecting a prime number?
    13·1 answer
  • Please help I don't understand it​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!