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seraphim [82]
2 years ago
8

Among a group of 100 people, 68 can speak English, 45 can speak French, 42 can speak Spanish. 27 can speak both English and Fren

ch, 25 can speak both English and Spanish, 16 can speak both French and Spanish, and 9 can speak all three languages. Pick a person at random from this group, what is the probability that this person can speak at least 1 of these languages?
Mathematics
1 answer:
Nat2105 [25]2 years ago
8 0

Answer:

Step-by-step explanation:

Given

No of People who can speak English is n(E)=68

No of People who can speak French is n(F)=45

No of People who can speak Spanish is n(S)=42

No of People who can speak both English and French n\left ( E\cap F\right )=27

No of People who can speak both English and Spanish n\left ( E\cap S\right )=25

No of People who can speak both French and Spanish n\left ( F\cap S\right )=16

No of people who can speak all languages is n\left ( E\cap F\cap S\right )=9

no of People who can Speak at least one Language is

n\left ( E\cup F\cup S\right )=n\left ( E\right )+n\left ( F\right )+n\left ( S\right )-n\left ( E\cap F\right )-n\left ( E\cap S\right )-n\left ( F\cap S\right )+n\left ( E\cap F\cap S\right )

n\left ( E\cup F\cup S\right )=68+45+42-27-25-16+9=96

Probability that Randomly selected can speak at least 1 of these languages

P=\frac{96}{100}=0.96

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Answer:

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Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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.

In this problem:

I will calculate the time in months. Each year has twelve months.

Mean shelf life is three years and four months, with a standard deviation of three months. So

\mu = 3*12 + 4 = 40

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Proportion lasting between three years and one month and three years and seven months:

This is the pvalue of Z when X = 3*12 + 7 = 43 subtracted by the pvalue of Z when X = 3*12 + 1 = 37

X = 43

Z = \frac{X - \mu}{\sigma}

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0.6826*25000 = 17,065

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