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Pie
2 years ago
9

Matilda recently took a statistics quiz in her math class. in one question, 45 of 900 visitors at a local craft show were survey

ed about the cost of admission to the show. Matilda incorrectly stated that the sample in this situation was represented by 900 visitors at the craft show.
a. what is Matilda's error?

b. what is the actual sample?
Mathematics
1 answer:
KonstantinChe [14]2 years ago
8 0

Answer: See explanation

Step-by-step explanation:

a. what is Matilda's error?

The error by Maltida was that she mistakenly thought the population was the sample size. In this case, the 900 visitors aren't the sample but the population.

The population is referred Tina's the entire pool where the sample is picked by the researcher.

b. what is the actual sample

The actual sample is 45. The sample is the smaller version which can be gotten from the entire population. It is a subset from the population of 900 visitors. Therefore, based on the question, it is 45.

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Answer:

a) 0.0523 = 5.23% probability that at least two of the four selected will turn to be no-shows.

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Step-by-step explanation:

For each traveler who made a reservation, there are only two possible outcomes. Either they show up, or they do not. The probability of a traveler showing up is independent of other travelers. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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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.

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And p is the probability of X happening.

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This means that p = 0.1

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This means that n = 4

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This is P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)

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P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001

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b) What is the most likely value for X?

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

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P(X = 1) = C_{4,1}.(0.1)^{1}.(0.9)^{3} = 0.2916

P(X = 2) = C_{4,2}.(0.1)^{2}.(0.9)^{2} = 0.0486

P(X = 3) = C_{4,3}.(0.1)^{3}.(0.9)^{1} = 0.0036

P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001

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