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Novosadov [1.4K]
3 years ago
12

Suppose you flip a coin and spin a spinner that is divided into 8 equal regions. Of the 8 equal regions, 3 are red, 4 are black

and 1 green. What is the probability of "tails" on the coin, and the spinner landing on red?
 (Hint: How many spaces are on the spinner total?)Immersive Reader
(5 Points)
Mathematics
1 answer:
atroni [7]3 years ago
7 0

Answer:

18.75%

Step-by-step explanation:

The probability of the coin is 1/2, because it only has two options (tail or head).

Now, in the case of roulette, it has a total of 8 options, and the red region has 3 parts, that is, of the 8 options, roulette 3 is red, therefore the probability is 3/8

Now the final probability is the multiplication of the probability of both events:

(1/2) * (3/8) = 0.1875 s 18.75%

In other words, the probability of these two events happening, that the tail comes out and is red, i

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z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05  

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Step-by-step explanation:

Data given and notation  

\bar X=34 represent the sample mean

\sigma=\sqrt{2.56}= 1.6 represent the population standard deviation

n=120 sample size  

\mu_o =33.7 represent the value that we want to test  

\alpha=0.02 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

System of hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is 33.7 mpg or no, the system of hypothesis would be:  

Null hypothesis:\mu =33.7  

Alternative hypothesis:\mu \neq 33.7  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05  

And the p value would be given by:

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And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.

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