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Strike441 [17]
2 years ago
14

A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over th

e next few weeks, and find that out 10 recommendations, he was correct 3 times. If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successfu
Mathematics
1 answer:
baherus [9]2 years ago
3 0

Answer:

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

p = 0.553, n = 10

If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:

This is

P(X \leq 4) = 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_{10,0}.(0.553)^{0}.(0.447)^{10} = 0.0003

P(X = 1) = C_{10,1}.(0.553)^{1}.(0.447)^{9} = 0.0039

P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219

P(X = 3) = C_{10,3}.(0.553)^{3}.(0.447)^{7} = 0.0724

P(X = 4) = C_{10,4}.(0.553)^{4}.(0.447)^{6} = 0.1567

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0003 + 0.0039 + 0.0219 + 0.0724 + 0.1567 = 0.2552

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

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Step-by-step explanation:

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The number of eggs in the refrigerator e decreased by 5 equals 18
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How many solutions exist for the given equation? 3x 13 = 3(x 6) 1 zero one two infinitely many
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<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation can be solved in the following manner,

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