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Strike441 [17]
3 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]3 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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There will be 36 squares in the 8th step of the pattern

<h3>How to determine the number of squares?</h3>

The pattern and the squares are represented as:

<u>Pattern   Squares</u>

1                 1

2                3

3               6

4             10

This can be rewritten as:

<u>Pattern   Squares</u>

1                 1

2                1 + 2

3                1 + 2 +3

4                1 + 2 + 3 +4

So, the number of squares on the 8th pattern is:

8th pattern = 1 + 2 + 3 +4 + 5 + 6 + 7 + 8

Evaluate

8th pattern = 36

Hence, there will be 36 squares in the 8th step

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3 0
2 years ago
Which Of The Following Rational Functions Is Graphed Below
Blizzard [7]

The given rational functions is graphed in the figure  is Option B. f(x) = 1/ ( x-2) (x + 5) is correct.

<h3>What is a function?</h3>

The function is a type of relation, or rule, that maps one input to specific single output.

Here, a graph is given.

We need to find which of the given rational functions is graphed in the figure.

On x-axis, 1 unit = 2 units

Clearly, we can see the graph is not defined at point x = 2 and at x = -5.

Corresponding to x = 2, factor is (x - 2) .

Corresponding to x = -5, factor is (x + 5) .

So, this graph is of the rational fraction

Hence, Option B. f(x) = 1/ ( x-2) (x + 5) is correct.

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5 0
2 years ago
Consider the figure. Determine the value of y.​
slava [35]

Answer:

47+ y = 180          (linear pair)

y = 133

6 0
3 years ago
Malachi bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sa
Volgvan

If the discount is 15 percent, he still pays (100-15) or 85%

125.99 * 85%

125.99 * .85 = 107.09  is the price he pays for the rod

107.09 * .03 =3.21 is the sales tax

107.09+3.21=110.30 is the price of the rod with the discount and the tax

8 0
3 years ago
A ferry is travelling at a constant speed back to the dock, as shown in the graph. Which
mario62 [17]

Answer:

c. y = -35*x + 105

Step-by-step explanation:

Lo que demos hacer es calcular los puntos cuando x = 0 y cuando x = 3, es decir el inicio y el fin del recorrido.

Cuando x es igual 0, y = 105, por lo tanto, la función sería:

y = A*x + 105

Cuando x = 3, y = 0, por lo tanto:

0 =  3*A +  105

resolvemos para A:

3*A =  -105

A = -105/3

A =  -35

Por lo tanto la función es:

y = -35*x + 105

es decir, la opción c.

7 0
3 years ago
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