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solniwko [45]
3 years ago
10

Find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one

trial is 9%.
Round to the nearest tenth of a percent
Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
6 0

Answer:

P(x \geq 6)=P(X=6)+P(X=7)

And we can find the individual probabilities:

P(X=6)=(7C6)(0.91)^6 (1-0.91)^{7-6}=0.358

P(X=7)=(7C7)(0.91)^7 (1-0.91)^{7-7}=0.517

And replacing we got:

P(x \geq 6)=P(X=6)+P(X=7)= 0.358+0.517=0.875

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=7, p=1-0.09=0.91)

The probability associated to a failure would be p =1-0.09 = 0.91

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

And we want to find this probability:

P(x \geq 6)=P(X=6)+P(X=7)

And we can find the individual probabilities:

P(X=6)=(7C6)(0.91)^6 (1-0.91)^{7-6}=0.358

P(X=7)=(7C7)(0.91)^7 (1-0.91)^{7-7}=0.517

And replacing we got:

P(x \geq 6)=P(X=6)+P(X=7)= 0.358+0.517=0.875

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Answer:

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Step-by-step explanation:

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Plug in the values

\frac{5}{10} = \frac{x + 5}{3x + 3}

Cross multiply

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Collect like terms

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6 0
3 years ago
Pls help I dont know how to do this​
german

Answer:

  • 1. CE = 63
  • 2. x = 16

Step-by-step explanation:

Use proportions to solve.

Corresponding sides have same ratio.

<u>Question 1</u>

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A radio station broadcasts a signal over qn area with a radius of 50 miles. The station can relay the signal and broadcast over
denpristay [2]
A = pi * r^2 
<span>A = 3.14 * 50^2 </span>
<span>A = 7,850 square miles (area of the 50 mile broadcast signal)

A = pi * r^2
A = 3.14 * 75^2
A = </span>17,662.5 = 17,663 square miles (area of the 75 mile relayed signal)

Now we just need to subtract the 50 mile signal from the 75 mile signal, so:

17,663 - 7,850 = <span>9,813 square miles greater


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