Hi i am Grace and i realllyyyyyy need help on this. If you could please help that would be great.

Mathematics

1 answer:

uranmaximum [27]3 years ago

7 0

The probability of picking a black ball first is $\dfrac{4}{5}$ , because there are 4 black balls and 1 white ball which is 5 balls in total. After picking the first ball, 4 balls remain - 3 black and 1 white, so the probability of picking a white ball is $\dfrac{1}{4}$ .
So, the probability of picking a black ball first followed by a white ball is $\dfrac{4}{5}\cdot\dfrac{1}{4}=\dfrac{1}{5}$

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Answer:

$(21.9-19.8) -1.966\sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 1.422$

$(21.9-19.8) -1.966 \sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 2.778$

And we are 95% confident that the true difference means are between $1.422 \leq \mu_1 -\mu_2 \leq 2.778$

Step-by-step explanation:

We know the following info:

$\bar X_1 = 21.9$ sample mean for group 1

$\bar X_2 = 19.8$ sample mean for group 2

$s_1 = 3.4$ sample standard deviation for group 1

$s_2 = 3.5$ sample standard deviation for group 2

$n_1 = 200$ sample size group 1

$n_2 = 200$ sample size group 2

We want to find a confidence interval for the difference of means and the correct formula to do this is:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

Now we just need to find the critical value. The confidence level is 0.95 then the significance is $1-0.95 =0.05$ and $\alpha/2 =0.025$ . The degrees of freedom are given by: