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joja [24]
3 years ago
15

How many different ways could a baking contest be judged if 15 pies are entered and 4 ribbons are awarded?

Mathematics
2 answers:
Rashid [163]3 years ago
8 0
This is a question of combination since it does not take into account the order of the pies. The answer would be 1365. There are 1365 ways a baking contest ways can be judged if 4 ribbons are awarded with 15 pie entries. 

In case you need the order, then the permutation answer would be 32760.
RoseWind [281]3 years ago
7 0

Answer:

1365

Step-by-step explanation:

We are given that 15 pies are entered in the contest.

Out of 15 , 4 are awarded with ribbons.

Now we are supposed to find How many different ways could a baking contest be judged.

Since the order of pie doesn't matter over here.

So, we will use combination.

^nC_r=\frac{n!}{r!(n-r)!}

Substitute n = 15

r = 4

So, ^{15}C_4=\frac{15!}{4!(15-4)!}

^{15}C_4=\frac{15!}{4!(11)!}

^{15}C_4=\frac{15 \times 14\times 13 \times 12 \times 11!}{4!(11)!}

^{15}C_4=\frac{15\times 14\times 13 \times 12}{4\times 3 \times 2\times 1}

^{15}C_4=1365

Hence there are 1365 ways in which a baking contest could be judged.

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Answer:

z=\frac{0.021 -0.012}{\sqrt{\frac{0.012(1-0.012)}{1655}}}=3.363  

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Step-by-step explanation:

Data given and notation

n=1655 represent the random sample taken

\hat p=0.021 estimated proportion of interest

p_o=0.012 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportions is higher than 0.012.:  

Null hypothesis:p \leq 0.012  

Alternative hypothesis:p > 0.012  

When we conduct a proportion test we need to use the z statisitic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.021 -0.012}{\sqrt{\frac{0.012(1-0.012)}{1655}}}=3.363  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.01. The next step would be calculate the p value for this test.  

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