If a ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability th
1 answer:
Answer:
a. 50%
b. 33%
c. 17% (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)
d. 67%
Step-by-step explanation:
a. We have a total of 18 balls, 13 are red and 5 are white. They are numbered from 1 to 18. In this case, we don't care about the color of the ball, we just need it to be not even. We have to count how many not even numbers are between 1 and 18, that is 9. So, the chances of getting a ball not even numbered are 9 in 18, that's
b. Now we do care about the color of the ball. The red balls are numbered from 1 to 13, so we have 6 balls even numbered. That makes the chances 6 in 18 (we still have 18 in total), that's
c. (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)
The white balls are numbered from 14 to 18, so we have 3 balls even numbered. That makes the chances 3 in 18,
d. Let's notice that "the ball is neither red or even numbered" is the complement (exactly the opposite) of "the ball is red and even numbered", that means
100% = Probability (ball red and even numbered) + Probability (ball neither red or even numbered)
So, Probability (ball neither red or even numbered) = 100% - Probability (ball red and even numbered) = 100% - 33% = 67%
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Hi there!
Let's first determine the x-intercept. When dealing with an x-intercept we must realise the y-coordinates equal 0.
Add 21 to both sides.
Divide both sides by -2.
Therefore, the x-intercept is the point (10 1/2; 0).
--------------------------------------
Now let's continue with the y-intercept, which is easier. When dealing with an y-intercept we must realise the x-coordinates equal 0.
Therefore, the y-intercept is the point (0; -21).
Let's first determine the x-intercept. When dealing with an x-intercept we must realise the y-coordinates equal 0.
Add 21 to both sides.
Divide both sides by -2.
Therefore, the x-intercept is the point (10 1/2; 0).
--------------------------------------
Now let's continue with the y-intercept, which is easier. When dealing with an y-intercept we must realise the x-coordinates equal 0.
Therefore, the y-intercept is the point (0; -21).
Answer:
a) (26.50;57.50)
b) (117.34;128.66)
c) (12.13;27.87)
d) (-4.73;11.01)
e) No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that is approximately normal, so the confidence intervals are valid
Step-by-step explanation:
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval is given by this formula:
(1)
And for a 95% of confidence the significance is given by , and
. Since we know the population standard deviation we can calculate the critical value
Part a
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (26.50;57.50)
Part b
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (117.34;128.66)
Part c
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (12.13;27.87)
Part d
If we use the formula (1) and we replace the values we got:
The 95% confidence interval is given by (-4.73;11.01)
Part e
No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that is approximately normal, so the confidence intervals are valid