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QveST [7]
2 years ago
14

You roll a six-sided die. Find the probability of each of the following scenarios

Mathematics
1 answer:
romanna [79]2 years ago
6 0

Answer:

a) 1/2

b) 5/6

c) 2/3

Step-by-step explanation:

a)

Rolling a number greater than 3 means you can roll a 4, 5, or 6, which contains rolling a 6. So, the probability is (1+1+1)/6=3/6=\boxed{1/2}

b)

Rolling a number less than 5 means you can roll a 1, 2, 3, or 4, but because you could also roll an even number, so you could also roll a 6.

So, the probability is (1+1+1+1+1)/6=\boxed{5/6}

c)

Rolling a 4 or an odd number means you can roll a 1, 3, 5, or 4. So, the probability is (1+1+1+1)/6=4/6=\boxed{2/3}

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The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15.
evablogger [386]

Answer:

4.4% of the population with IQ between 120 and 125.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.

a) Let X be a person's IQ score.

Then, density functions for IQ scores is given by:

P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{z^2}{2}}\\\\\text{where,}\\\\z = \frac{x-\mu}{\sigma}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-100)^2}{450}}

b) P(population with IQ between 120 and 125.)

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(120 \leq x \leq 125) = P(\displaystyle\frac{120 - 100}{15} \leq z \leq \displaystyle\frac{125-100}{15}) = P(1.33 \leq z \leq 1.66)\\\\= P(z \leq 1.66) - P(z < 1.33)\\= 0.952 - 0.908 = 0.044 = 4.4\%

P(120 \leq x \leq 125) = 4.4\%

6 0
2 years ago
A crew must repave a road that is 3/8 miles long. They can repave 1/48 miles per hour. How long will it take the crew to repave
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Answer:

Step-by-step explanation:

3/8 miles long, 1/48 miles per hour

3/8 and 1/48 can have a common denominator, so you make 3/8 into 18/48 by multiplying both the numerator and denmoinator by 6.

18/48 miles long

1/48 per hour

divide: 18/48 divided by 1/48, which turns into 18/48 x 48/1 which equals 18

18 hours

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Rou<br>Round 66.681 to the nearest ten thousand.​
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Answer:

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Step-by-step explanation:

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