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alekssr [168]
3 years ago
9

The cable company is analyzing the data from two satellite television providers to determine whether their users spend more time

watching live television or shows that have been recorded.
Satellite Company X: 89 live, 430 recorded
Satellite Company Y: 65 live, 94 recorded

To the nearest whole percent, what is the probability that a randomly selected customer from Satellite Company Y watches recorded shows more often than live television?
Mathematics
2 answers:
Kamila [148]3 years ago
8 0
Probability that a Satellite Company Y watches a recorded show 
<span>= Py(recorded) </span>
<span>= 94/159 </span>
<span>= 0.59119 </span>
<span>= 59.12% </span>
<span>≈ 59% (Rounded to the nearest percent)................ANS</span>
Kruka [31]3 years ago
5 0

Answer: 59%

Step-by-step explanation:

From the given table, the number of customer from Satellite Company Y  spend more time watching shows that have been recorded =94

The total number of customers from Satellite Company Y =65+94=154

Now, the probability that a randomly selected customer from Satellite Company Y watches recorded shows more often than live television =\frac{94}{159}

In percent, \frac{94}{159}\times100=59.1194968553\%\approx59\%

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natta225 [31]

Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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.

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

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

P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

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

P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

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