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BartSMP [9]
3 years ago
15

For a binomial distribution with p = 0.20 and n = 100, what is the probability of obtaining a score less than or equal to x = 12

? hint: use interval-based calculations because no critical region is involved.​
Mathematics
1 answer:
notsponge [240]3 years ago
7 0
The binomial distribution is given by, 
P(X=x) =  (^{n}C_{x})p^{x} q^{n-x}
q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability <span>of obtaining a score less than or equal to 12.
</span>∴ P(X≤12) = (^{100}C_{x})(0.2)^{x} (0.8)^{100-x}
                    where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12                  
∴ P(X≤12) = (^{100}C_{0})(0.2)^{0} (0.8)^{100-0} + (^{100}C_{1})(0.2)^{1} (0.8)^{100-1} + (^{100}C_{2})(0.2)^{2} (0.8)^{100-2} + (^{100}C_{3})(0.2)^{3} (0.8)^{100-3} + (^{100}C_{4})(0.2)^{4} (0.8)^{100-4} + (^{100}C_{5})(0.2)^{5} (0.8)^{100-5} + (^{100}C_{6})(0.2)^{6} (0.8)^{100-6} + (^{100}C_{7})(0.2)^{7} (0.8)^{100-7} + (^{100}C_{8})(0.2)^{8} (0.8)^{100-8} + (^{100}C_{9})(0.2)^{9} (0.8)^{100-9} + (^{100}C_{10})(0.2)^{10} (0.8)^{100-10} + (^{100}C_{11})(0.2)^{11} (0.8)^{100-11} + (^{100}C_{12})(0.2)^{12} (0.8)^{100-12}


Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability. 
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Step-by-step explanation:

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bixtya [17]

Answer:

The percentage is <u>55%</u> when weight limit is 33 pounds.

The percentage is <u>190%</u> when weight limit is 114 pounds.

The 95% of the limit weighs <u>57</u> pounds.

Step-by-step explanation:

Given:

Weight limit of rocking horse = 60 pounds.

We need to find:

a) What percentage of the weight limit is 33 pounds.

b)What percentage of the weight limit is 114 pounds.

c) What weight is 95% of the limit.

Now Solving for a we get;

Weight limit = 33 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = \frac{33}{60}\times100 = 55\%

Hence The percentage is <u>55%</u> when weight limit is 33 pounds.

Now Solving for b we get;

Weight limit = 114 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = \frac{114}{60}\times100 = 190\%

Hence The percentage is <u>190%</u> when weight limit is 114 pounds.

Now Solving for c we get;

Percentage Weight = 95%

Now Amount of weight limit can be calculated by multiplying Percentage weight limit with total weight limit and then Dividing by 100 we get;

framing in equation form we get;

percentage of the weight limit = \frac{95}{100}\times60 = 57 \pounds

Hence The 95% of the limit weighs <u>57</u> pounds.

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Answer:

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Answer:

A

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