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3 years ago

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There are 27 chocolates in a box, all identically shaped. There 4 are filled with nuts, 8 with caramel, and 15 are solid chocola

te. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a solid chocolate candy followed by a nut candy.

1 answer:

AlekseyPX3 years ago

6 0

Answer:

Therefore the required probability is $\frac{30}{351}$ .

Step-by-step explanation:

Two events are dependents event if the occurrence of one of them has effect on the probability of the other.

If A and B are dependents,

then,

P(AB)=P(A)P(B).

Given that,

There are 27 chocolates in a box.

Number of nuts chocolates = 4

Number of caramel chocolates = 8

Number of solid chocolates= 15.

The probability of that a solid candy is drawn is

$=\frac{\textrm{Number of solid chocolate}}{\textrm{Total number of chocolate}}$

$=\frac{15}{27}$ .

After selecting a solid chocolate, the number of chocolate is= (27-1)=26.

The probability that a nut candy is drawn is

$=\frac{\textrm{Number of nut chocolate}}{\textrm{Total number of chocolate}}$

$=\frac{4}{26}$

$=\frac{2}{13}$

Therefore the required probability is

$=\frac{15}{27}\times\frac{2}{13}$

$=\frac{30}{351}$

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A random sample of n = 40 observations from a quantitative population produced a mean x = 2.2 and a standard deviation s = 0.29.

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Answer:

$t=\frac{2.2-2.1}{\frac{0.29}{\sqrt{40}}}=2.18$

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_{(39)}>2.18)=0.0177$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and then the population mes seems to be higher than 2.1 at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X=2.2$ represent the sample mean

$s=0.29$ represent the sample standard deviation

$n=40$ sample size

$\mu_o =2.1$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 2,1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.1$

Alternative hypothesis: $\mu > 2.1$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{2.2-2.1}{\frac{0.29}{\sqrt{40}}}=2.18$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_{(39)}>2.18)=0.0177$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and then the population mes seems to be higher than 2.1 at 5% of significance

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The number of those who attended the picnic was 8.

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Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.

Let x represent the whole population.

Total Spending = Rs. 96

Thus, each individual's contribution is equal to 96/x.

Four people did not show up causing

others to contribute Rs. 4 extra.

So the given condition can be written as

96/(x-4) – 96/x = 4

=>96x – 96(x-4) = 4x(x-4)

=> 96x -96x + 384 = 4x2 – 16x

=> 4x2 – 16x – 384 = 0

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=> x = 12 or x = -8 (neglect)

So x = 12

x-4 = 8 ( because four of them did not turn up)

∴ The number of those who attended the picnic was 8.

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