HELP PLS! At a raffle, 100 tickets are sold for 1 prize of $100 and 3 consolation prizes of $20. What prizes should the tickets
1 answer:
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Answer:
11.51% probability that it will take less than 450 days to train all the contestants.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n variables, the mean is and the standard deviation is
In this question:
Approximate the probability that it will take less than 450 days to train all the contestants.
This is the pvalue of Z when X = 450.
By the Central Limit Theorem
has a pvalue of 0.1151
11.51% probability that it will take less than 450 days to train all the contestants.
The correct answer is: [B]: " 22 " .
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Explanation:
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Given:
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;
Solve when: "n = 3" ;
Rewrite the expression; substituting "3" for all values of "n" ; as follows:
→
;
The "6" cancels out to "2" ; & the "3" cancels out to "1" ;
→ {since: " {6 ÷ 3 = 2}" ; and since: " {2 ÷ 2 = 1}" .
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→ Since the "denominator" is "1" ; and any value, divided by "1"; results in that original value; we can eliminate the denominator.
→ Now, we can rewrite the expression as:
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→ " 2(3² + 2)" ;
= 2(9 + 2) ;
= 2(11) ;
= " 22 " .
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→ The answer is: " 22 " ; which is: Answer choice: [B]: " 22 " .
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_________________________________________________________
Explanation:
_________________________________________________________
Given:
_________________________________________________________
Solve when: "n = 3" ;
Rewrite the expression; substituting "3" for all values of "n" ; as follows:
→
The "6" cancels out to "2" ; & the "3" cancels out to "1" ;
→ {since: " {6 ÷ 3 = 2}" ; and since: " {2 ÷ 2 = 1}" .
_________________________________________________________
→ Since the "denominator" is "1" ; and any value, divided by "1"; results in that original value; we can eliminate the denominator.
→ Now, we can rewrite the expression as:
_________________________________________________________
→ " 2(3² + 2)" ;
= 2(9 + 2) ;
= 2(11) ;
= " 22 " .
_________________________________________________________
→ The answer is: " 22 " ; which is: Answer choice: [B]: " 22 " .
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