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horrorfan [7]
3 years ago
6

You roll a 6-sided die. Find the P(4).

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
6 0
Because all outcomes are equally weighted, the probability you are looking for is given by :-
Number of favorable eventsTotal number of events
Number of favorable events
Total number of events

In your case: 6 or Even outcome={2,4,6}
6
or Even outcome
=
{
2
,
4
,
6
}
and Outcomes={1,2,3,4,5,6}
Outcomes
=
{
1
,
2
,
3
,
4
,
5
,
6
}

Hence:

Number of favourable eventsTotal number of events=36=12
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A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small
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Answer:

95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.

Step-by-step explanation:

Confidence interval is given by mean +/- margin of error (E)

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Sample size (n1) = 60

Mean = 37.2

Sample variance = 24.7

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Sample size (n2) = 159

Mean = 35.6

Sample variance = 39

Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11

Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93

Difference in mean = 37.2 - 35.6 = 1.6

Degree of freedom = n1+n2 - 2 = 60+159-2 = 217

Confidence level = 95%

Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132

E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79

Lower limit = mean - E = 1.6 - 0.79 = 0.81

Upper limit = mean + E = 1.6 + 0.79 = 2.39

95% confidence interval for the difference in average mass is (0.81, 2.39)

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