You roll a pair of fair six-sided dice. The sample space of 36 possible outcomes is shown below. Based on this information, answ
1 answer:
Answer:
All the 36 outcomes are equally likely.
Step-by-step explanation:
The sample space of rolling a single six-sided dice is:
S = {1, 2, 3, 4, 5, 6}
Then the sample space of rolling a pair of six-sided dice is:
S₁ = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
All the 36 outcomes are equally likely, i.e. all the outcomes has the same probability of success, .
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Answer:
The confidence interval estimate of the population mean is :
(0.61 ppm, 0.90 ppm)
The correct option is (A).
Step-by-step explanation:
The amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city are:
S = {0.58, 0.82, 0.10, 0.98, 1.27, 0.56, 0.96}
A confidence interval for the population mean (μ) is an interval estimate of the true value of the mean. This interval has a
probability of consisting the true value of mean.
⇒ Since the population standard deviation is not provided we will use the <em>t</em>-distribution to construct the 99% confidence interval for mean.
⇒ The formula for confidence interval for the population mean is:
Here,
= sample mean
<em>s </em>= sample standard deviation
<em>n</em> = sample size
= critical value.
The degrees of freedom for the critical value is, (<em>n</em> - 1) = 7 - 1 = 6.
The significance level is:
The critical value is:
**Use the <em>t</em>-table for the critical value.
Compute the sample mean and sample standard deviation as follows:
The 99% confidence interval for μ is:
The confidence interval estimate of the population mean is:
(0.61 ppm, 0.90 ppm)
The upper and lower limit of the 99% confidence interval indicates that the true mean value is less than 1 ppm. This implies that there is not too much mercury in tuna sushi
Because it is possible that the mean is not greater than 1 ppm. Also, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.
Thus, the correct option is (A).
Answer:
As long as the sample size n is large enough: The average IQ of Americans in the sample will be normally distributed.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
So the correct answer is:
As long as the sample size n is large enough: The average IQ of Americans in the sample will be normally distributed.