A bag contains 9 red marbles,7 blue marbles, and 4 green marbles. A randomly drawn marble is blue?

Mathematics

1 answer:

Elena-2011 [213]3 years ago

3 0

Answer: $\frac{7}{20}$

Step-by-step explanation:

If this is asking for the probability of randomly drawing a blue marble then it'll be however many blue marbles (what you're trying to find) out of the total number of marbles

Blue marbles: 7

Total marbles: 20

$\frac{7}{20\\}$

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"4. A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of de

SSSSS [86.1K]

Answer:

With a 0.01 significance level and samples of 50 and 40 cofee drinkers, there is enough statistical evidence to state that the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers.

The test is a one-tailed test.

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the difference of population means.

$$$Sample mean $\bar X: \bar X=4.35$\\Sample mean $\bar Y: \bar Y=5.84$\\Population variance $\sigma^2_X: \sigma^2_X=1.2^2$\\Population variance $\sigma^2_Y: \sigma^2_Y=1.36^2$\\Sample size $n_X=50$\\Sample size $n_Y=40$\\Significance level $\alpha=0.01$\\Z criticals values (for a 0.01 significance)\\(Left tail test) Z_{1-\alpha}=Z_{0.990}=-2.32635\\($Right tail test) Z_{\alpha}=Z_{0.010}=2.32636\\($Two-tailed test) $Z_{1-\alpha/2}=Z_{0.995}=-2.57583$ and $ Z_{\alpha/2}=Z_{0.005}=2.57583\\\\$

The appropriate hypothesis system for this situation is:

$H_0: \mu_X-\mu_Y=0\\H_a: \mu_X-\mu_Y \leq 0\\\\$

Difference of means in the null hypothesis is:

$\mu_X - \mu_Y = M_0=0\\\\$

$$$The test statistic is$ Z=\frac{( \bar X-\bar Y)-M_0}{\sqrt{\frac{\sigma^2_X}{n_X}+\frac{\sigma^2_Y}{n_Y}}}\\$ $$$The calculated statistic is Z_c=\frac{[(4.35-5.84)-0]}{\sqrt{\frac{1.20^2}{50}+\frac{1.36^2}{40}}}=-5.43926\\p-value = P(Z \leq Z_c)=0.0000\\\\$

Since, the calculated statistic $Z_c$ is less than critical $Z_{1-\alpha}$ , the null hypothesis should be rejected. There is enough statistical evidence to state that the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers.