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Scrat [10]
2 years ago
14

At a carnival, contestants are asked to keep rolling a pair of dice until they roll snake eyes. The number of rolls needed has a

mean of 36 rolls, with a standard deviation of 5.4 rolls. The distribution of the number of rolls needed is not assumed to be symmetric.
Between what two numbers of rolls does Chebyshev's Theorem guarantee that we will find at least 75% of the contestants?
Mathematics
1 answer:
Stells [14]2 years ago
8 0

Answer:

The two numbers of rolls are 25.2 and 46.8.

Step-by-step explanation:

The Chebyshev's theorem states that, if X is a r.v. with mean µ and standard deviation σ, then for any positive number k, we have  

P (|X -\mu| < k\sigma) \geq  (1-\frac{1}{k^{2}})

Here

(1-\frac{1}{k^{2}})=0.75\\\\\Rightarrow \frac{1}{k^{2}}=0.25\\\\\Rightarrow k=\sqrt{\frac{1}{0.25}}\\\\\Rightarrow k=2

Then we know that,

|X - \mu| \geq k\sigma,\\\\  \Rightarrow \mu - k\sigma \leq X \leq \mu + k\sigma.

Here it is given that mean (µ) = 36 and standard deviation (σ) = 5.4.

Compute the two values between which at least 75% of the contestants lie as follows:

P(\mu - k\sigma \leq X \leq \mu + k\sigma)=0.75\\\\P(36 - 2\cdot\ 5.4 \leq X \leq 36 + 2\cdot\ 5.4)=0.75\\\\P(25.2\leq X\leq 46.8)=0.75

Thus, the two numbers of rolls are 25.2 and 46.8.

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Answer:

The equation would be y = x + 5, in which x is the number of weeks and y is the number of books he has.

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We know this because even at 0 weeks, he still has 5 books. Therefore we put this as the constant at the end. Then we can add the number of weeks since the rate is one book per week.

5 0
3 years ago
Write three different equations that have x=5 as a solution
svlad2 [7]

Answer: The three different equations will be

x+3=8\\\\2x-8=2\\\\4x-4=16

Step-by-step explanation:

We have to write three equation that have x = 5 as a solution:

1) First equation will be

x+3=8\\\\x=8-3\\\\x=5

2) Second equation will be

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3) Third equation will be

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Hence, the three different equations will be

x+3=8\\\\2x-8=2\\\\4x-4=16



7 0
3 years ago
Read 2 more answers
Write the first four terms of the sequence:<br> a = 2<br> an = a(n-1) + 4
eduard

We have sequence equation a_n=a(n-1)+4.

In this case n is a natural number (1, 2, 3, ...).

So start inserting and computing value of a_n given that you know the value of n and a.

a_1=2(1-1)+4=4 (first term)

a_2=2(2-1)+4=6 \\a_3=2(3-1)+4=8 \\a_4=2(4-1)+4=10

Hope this helps.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Multiply

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3 years ago
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