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
blondinia [14]
3 years ago
11

As reported in Trends in Television, the proportion of US households who have at least one VCR is 0.535. If 14 households are se

lected at random, without replacement, from all US households, what is the (approximate) probability that the number having at least one VCR is no more than 8 but at least 6.00. Be sure to use many decimal places in your calculations (at least 4), but report your answer to three decimal places.
Mathematics
1 answer:
motikmotik3 years ago
8 0

Using the binomial distribution, it is found that there is a 0.5601 = 56.01% probability that the number having at least one VCR is no more than 8 but at least 6.00.

For each household, there are only two possible outcomes. Either it has at least one VCR, or it does not. The probability of a household having at least one VCR is independent of any other household, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 14 households, hence n = 14.
  • 0.535 probability of having at least one VCR, hence p = 0.535.

The probability of <u>at least 6 and no more than 8</u> is:

P(6 \leq X \leq 8) = P(X = 6) + P(X = 7) + P(X = 8)

In which:

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

P(X = 6) = C_{14,6}.(0.535)^{6}.(0.465)^{8} = 0.1539

P(X = 7) = C_{14,7}.(0.535)^{7}.(0.465)^{7} = 0.2024

P(X = 8) = C_{14,8}.(0.535)^{8}.(0.465)^{6} = 0.2038

Then:

P(6 \leq X \leq 8) = P(X = 6) + P(X = 7) + P(X = 8) = 0.1539 + 0.2024 + 0.2038 = 0.5601

0.5601 = 56.01% probability that the number having at least one VCR is no more than 8 but at least 6.00.

A similar problem is given at brainly.com/question/24863377

You might be interested in
Dress works in a factory that makes combs. He discovered that out of 500 combs, 34 of those are defective. If the factory produc
Bingel [31]

Answer: 175

Step-by-step explanation: First, a group of five hundred combs produces 34 defective combs. So if they make 2,500, you multiply how many times you add 500 to get to 2,500, which should be 5. Now multiply that to 34 and you get 175! To check it, divide: 34 divide by 150. Hope this helps!

6 0
3 years ago
Maryland had $(62xsquared + x - 4) on mondays she spent $(11x squared - 33) on a pair of gloves how much money did she have left
Anton [14]

Answer:

$( 51x^2 + x + 29).

Step-by-step explanation:

Amount she had left = original amount - amount spent on the gloves

=  62x^2 + x - 4 - (11x^2 - 33)   (note we place the amount spent on gloves in parentheses because we have to subtract the whole amount)

Now we distribute the negative over the parentheses:

= 62x^2 + x - 4 - 11x^2 + 33     ( note - 33 becomes -33*-1 = +33)

Now simplifying like terms:

= 51x^2 + x + 29  (answer).

7 0
3 years ago
Simplify Simplify 6 - 23 + (-9 + 5) · 2.
Vlad [161]

Answer:

The answer is −42

7 0
3 years ago
Find the product.<br><br>(0.5n 5)2(10n 7) 3
sergejj [24]
Your product would be
(0.5n5)2(10n7)3
7 0
3 years ago
Read 2 more answers
Tony works 22 hours per week. His take home pay is $15.80 per hour. If Tony is able to save all of his earnings, how long will i
denis23 [38]
About 14 weeks to reach 4800
4 0
3 years ago
Read 2 more answers
Other questions:
  • Find 2 a for a = 3 1/4<br> 1) 6 1/2<br> 2) 6 1/4<br> 3) 23 1/4<br> 4) 5 1/2
    7·1 answer
  • Are the following figures similar?
    11·1 answer
  • Compare the values of the underline digits. 2,402 and 64,513   the value of 4 in _______________ is _______ times the values of
    6·1 answer
  • What is the answer to this question
    15·2 answers
  • How do I factor 25n^2 - 16?
    7·1 answer
  • Round 7782 to the nearest hundred round 992449 to the nearest hundred thousand
    9·1 answer
  • Pls helpp<br> Write the expression using exponents.<br> b.b.b = ?
    7·2 answers
  • Please help me wiyh this<br> In triangle △WXY, XY ≅ WX and m∠X=38 Find m∠W
    5·1 answer
  • 177 ×44 Please hurry but take your time​
    12·2 answers
  • What is equivalent <br><br> 2r+(t+r)2
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!