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In a large population, about [tex]$45 \%$[/tex] of people prefer tea over coffee. A researcher takes a random sample of 13 people and surveys whether they prefer tea over coffee.

Use the binomial distribution to compute the probability that exactly 6 of the people in the sample prefer tea over coffee.

Identify the following information required to find the probability of people who prefer tea over coffee.

Provide your answer below:

[tex]\[ n = \square \text{ trials} \][/tex]
[tex]\[ x = \square \text{ successes} \][/tex]
[tex]\[ p = \square \text{ probability of those who prefer tea (as a decimal, not percent)} \][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's identify the given information required to find the probability of people preferring tea over coffee using the binomial distribution.

1. The number of trials ([tex]$n$[/tex]) represents the total number of people surveyed.
2. The number of successes ([tex]$x$[/tex]) represents the number of people in the sample who prefer tea over coffee.
3. The probability of success ([tex]$p$[/tex]) represents the probability that a single person prefers tea over coffee.

Given:
- The number of trials ([tex]$n$[/tex]) is 13.
- The number of successes ([tex]$x$[/tex]) is 6.
- The probability of success ([tex]$p$[/tex]) is 0.45 (as a decimal).

So, we have the following information:

[tex]$n = 13$[/tex] trials \\
[tex]$x = 6$[/tex] successes \\
[tex]$p = 0.45$[/tex] probability of those who prefer tea (as a decimal, not percent)
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