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
Anna11 [10]
3 years ago
8

According to the last census (2010), the mean number of people per household in the United States is LaTeX: \mu = 2.58 Assume a

standard deviation of LaTeX: \sigma = 0.75σ = 0.75. You plan to take a random sample of 110 households, what is the probability the sample mean household size is between 2.5 and 2.66 people? (round your probabilities to three decimal places)
Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
7 0

Answer:

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, \mu = 2.58 and Standard deviation, \sigma = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

             Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar \leq 2.50)

P(Xbar < 2.66) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{2.66-2.78}{\frac{0.75}{\sqrt{110} } } ) = P(Z < -1.68) = 1 - P(Z  1.68)

                                                              = 1 - 0.95352 = 0.04648

P(Xbar \leq 2.50) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{2.50-2.78}{\frac{0.75}{\sqrt{110} } }  ) = P(Z \leq  -3.92) = 1 - P(Z < 3.92)

                                                              = 1 - 0.99996 = 0.00004  

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

You might be interested in
Which statement correctly describes this expression?<br> 2m^3 - 11
Nady [450]

Answer:

<h2>D</h2>

The cube of twice a number decreased by 11

6 0
3 years ago
What is the Square root of 485?
algol [13]

22.0227155455


Good day!

5 0
3 years ago
Read 2 more answers
Kira's store collects 5% sales tax on every item sold. If she collected $22 in sales tax, what was the cost of the items her sto
Hatshy [7]

Answer:

48

Step-by-step explanation:

7 0
3 years ago
HELP! Find the value of the 30th percentile of the following set of data. 129, 113, 200, 100, 105, 132, 100, 176, 146, 152
BlackZzzverrR [31]
Let list the data in ascending order 100, 100, 105, 113, 129, 132, 146, 152, 176, 200

There are ten numbers so the thirtieth percentile would be the .3 * 10 

= 3rd number, ordered from smallest to largest. 

so the third number, the thirtieth percentile, is 105

7 0
3 years ago
There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once.
pychu [463]

Answer:

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen.          Here the card is chosen with replacement.  This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.

The sample space= {1,2,3,4,5,6,7,8,9,10}

Prime numbers = {2,3,5,7}

Prob for drawing prime number = 4/10 = 0.4

is the same when replacement is done.

Also there are two outcomes either prime or non prime.  Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5


When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.

Prob for an even number = 0.5

But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other.  Hence not binomial.

When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3

i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.

When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen

Here X is the number of times a card is chosen with replacement till 5 is chosen.  This is not binomial.  Here probability for drawing nth time correct 5 is  P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)

Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.

Step-by-step explanation:


6 0
3 years ago
Other questions:
  • If a well pumps at a rate of 8.4 gal per minute, how long would it take to fill the tank described above?
    6·1 answer
  • Which expression is equivalent?
    9·1 answer
  • A swimming pool is in the shape of a rectangular prism. It measures 15 feet by 12 feet by 8 feet. How many cubic feet of water a
    15·2 answers
  • Has an x-intercept of (4,0) and a y- intercept of (0,-2)
    10·1 answer
  • Can someone help me with this problem that is in the picture
    10·2 answers
  • Sara shaded 2/10 of a piece of grid paper. Derrick shaded 45/100
    7·1 answer
  • Y = 2/3x - 2<br> y = -x + 3<br> Please and quickly
    13·1 answer
  • Y=3x+2 i need a graph for this
    10·1 answer
  • Challenge A cell phone plan costs $19.80 per month for 400 minutes of talk time. It costs an additional $0.06 per minute for eac
    9·1 answer
  • Please I really need help, and please don't try and play me becasue someone just put the wrong answer and juked 70 of my points
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!