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
shusha [124]
3 years ago
14

At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is . 43. Find the proba

bility that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.
Mathematics
1 answer:
Ne4ueva [31]3 years ago
5 0

Answer:

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they order a nonalcoholic beverage, or they order an alcoholic beverage. The probability of a customer ordering a nonalcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.43.

This means that p = 0.43

Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

This is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{7,0}.(0.43)^{0}.(0.57)^{7} = 0.0195

P(X = 1) = C_{7,1}.(0.43)^{1}.(0.57)^{6} = 0.1032

P(X = 2) = C_{7,2}.(0.43)^{2}.(0.57)^{5} = 0.2336

P(X = 3) = C_{7,3}.(0.43)^{3}.(0.57)^{4} = 0.2937

P(X = 4) = C_{7,4}.(0.43)^{4}.(0.57)^{3} = 0.2216

Then

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0195 + 0.1032 + 0.2336 + 0.2937 + 0.2216 = 0.8716

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

You might be interested in
Please help ASAP!!!!!!!!!!
Minchanka [31]

well if 200 people entered the stadium then divide that number by 27

4 0
3 years ago
What is the unit rate of $112 in 8 hours
Andreyy89
It is 62.54
 Hope this helped.
6 0
3 years ago
Select the best answer for the question
Usimov [2.4K]

Answer:

its 72%

Step-by-step explanation:

7 0
3 years ago
4x/3=8 what is x? PLEASE HURRY DUE TOMORROW!!!!!!
DENIUS [597]

Step-by-step explanation:

4x=3×8

4x=24

x=24÷4

x=6

7 0
3 years ago
I need help on problem number 6 and 8 plzzzz
katrin [286]
For 6 I think it was B I am not so sure. Its been a long time since i did triangles
3 0
3 years ago
Read 2 more answers
Other questions:
  • Asking for help on this bad boy
    9·2 answers
  • The surface area of a cone with radius r units and slant height s units is shown below:
    9·2 answers
  • Ms.Jonhson and Ms.Siple were folding report cards to send home to parents. The ratio of number of report cards Ms.Jonhson folded
    12·1 answer
  • Cone A has a radius 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the volume of Cone A if 48, fin
    11·2 answers
  • How can graphing methods be used to solve a system of linear equations and how can you determine the equations of the two lines
    8·1 answer
  • A right triangle has an area of 24ft^2. The dimensions of the triangle are increased by a scale factor of 6. What is the area of
    8·1 answer
  • The speed of a fish before jumping out of the water can be represented by the equation s = 3h, where h
    14·1 answer
  • A)Solve for x: <br> y = 130 − 4x<br><br> b) What is the value of x when y = 120
    7·1 answer
  • Linear Equation: y = 5x + 5 No links please!
    6·1 answer
  • Mindy gets 3 dollars a week for allowance. She saved all of her allowance for 10 weeks, and then she bought a shirt for 24 dolla
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!