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qaws [65]
3 years ago
11

In the locker room, there are 8 rows of 9 lockers. All lockers were full in the morning, but in the afternoon 6 were empty. How

many lockers were full in the afternoon?​
Mathematics
1 answer:
anastassius [24]3 years ago
6 0

Answer:

66

Step-by-step explanation:

The total number of lockers that were full in the morning was 72. Since 6 were empty in the afternoon, 72-6 = 66 full lockers

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Find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one
oksano4ka [1.4K]

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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