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
Nataly [62]
3 years ago
13

We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty

18-20 year olds. 1. How many people would you expect to have consumed alcoholic beverages? (round to one decimal place) 2. What is the standard deviation? (round to two decimal places) 3. Would you be surprised, if there were 45 or more people who have consumed alcoholic beverages? _
Mathematics
1 answer:
maw [93]3 years ago
6 0

Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let <em>X</em> = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable <em>X</em> is, <em>p</em> = 0.697.

A random sample of <em>n</em> = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 50 and <em>p</em> = 0.697.

The probability mass function of a Binomial random variable <em>X</em> is:

P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...

(1)

Compute the expected value of <em>X</em> as follows:

E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of <em>X</em> as follows:

SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of <em>X</em> ≥ 45 as follows:

P (<em>X</em> ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

                =\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. <em>p</em> < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

You might be interested in
How do you solve ? <br>2(x−(3+2x)+9)=3x−8
PIT_PIT [208]

Hey there!!

Given equation :

... 2 ( x - ( 3 + 2x ) + 9 ) = 3x - 8

Using the distributive property.

... 2 ( x - 3 - 2x + 9 ) = 3x - 8

... 2 ( -x + 6 ) = 3x - 8

Using the distributive property.

... -2x + 12 = 3x - 8

Subtracting 12 on both sides.

... -2x = 3x - 8 - 12

... -2x = 3x - 20

Subtracting 3x on both sides.

... -2x - 3x = -20

... -5x = -20

Dividing by -5 on both sides.

... x = -20 / -5

... x = 4

<em>Hence, the answer is 4. </em>

Hope my answer helps!

6 0
3 years ago
What is the proof for this?
Butoxors [25]
Knowing nexnjhdjhdhfgnu. Hngj
5 0
3 years ago
Multiply. 4 × 16.7....
DaniilM [7]

Answer:

66.8

Step-by-step explanation:

Try only multiplying 16 and 4, then 0.7 and 4, then add them all up.

4 0
3 years ago
A yogurt cost 55 p . <br> how many yogurts can be brought for six pound ?
lions [1.4K]

Answer:

Since 3 pounds would get you 5 yogurts multiply that by two and you get 10

The answer is 10 yogurts

Hope it helped!

Step-by-step explanation:

4 0
3 years ago
Line WX and line YZ intersect at point V. If angle WVY = 4a + 58 and angle XVY = 2b - 18, find the values of a and b so that lin
amid [387]

we know that

If line WX is perpendicular to line YZ

then

see the attached figure to better understand the problem

m∠WVY=90°--------> 4a+58=90-----> 4a=90-58-----> a=32/4------> a=8°

m∠XVY=90°--------> 2b-18=90----> 2b=90+18------> b=118/2-------> b=59°

therefore

<u>the answer is</u>

a) The value of a is 8 degrees

b) The value of b is 59 degrees

5 0
3 years ago
Other questions:
  • Explain how to right 50,000 as a exponents
    12·1 answer
  • An equation is shown.<br> 18+ 5(2x + 5) = 12<br> Solve the equation for x.
    15·1 answer
  • PLEASE HELP THIS IS THE LAST QUESTION!!
    6·1 answer
  • a factory produces 30480 bolts in 12 hours. if the same number of bolts are produced each hour, how many bolts does the factory
    11·1 answer
  • What is the answer to 4.0×10^7m in standard form
    15·1 answer
  • What is 83/9 as a mixed number
    14·1 answer
  • Order these in descending order (greatest to least). 3/20, 0.15%, 0.015
    9·1 answer
  • What is the mean of the data?
    10·1 answer
  • Name the corresponding angle or side. a, b, c, or D
    8·1 answer
  • What is the answer to the fraction equation: 2/3+5/6÷1/3?<br> ​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!