Question

In a certain town,20% samples of the population is literate and assume that 200 investigators take samples of ten individuals to see whether they are literate. How many investigators would you expect to report that 3 people or less and literates in the samples?

Answer 1

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Step-by-step explanation:

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Answer 2

176 investigators would report that 3 people or less are literates in the samples.

Given - Literate population percentage and number of investigators

Find - Number of investigators with required report

Solution - The probability of chosen person is literate = 20/100

Probability of choosing literate person = 1/5

Probability of choosing illiterate person =

1 - (1/5)

Taking LCM and performing subtraction

Probability of choosing illiterate person =

((1*5) - 1)/5

Probability of choosing illiterate person =

4/5

Now, Probability of expecting 3 or less literate person in a sample of 10.

Probability = ${ \frac{4}{5} }^{10} + {C1} ^{10} { \frac{4}{5} }^{9} \frac{1}{5} + {C2} ^{10} { \frac{4}{5} }^{8} {\frac{1}{5}}^{2} + {C3} ^{10} { \frac{4}{5} }^{7} {\frac{1}{5}}^{3}$

= 1048576/9765625 + 524288/1953125 + 589824/1953125 + 393216/1953125

= 8585216/9765625

= 0.879

The expected number of investigators would be = 200*0.879

Performing multiplication

The expected number of investigators would be = 175.8

Hence, the expected number of investigators would be 176.

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