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An employment agency required 20 secretarial candidates to type the same manuscript. The number of errors found in each manuscript is summarized in the histogram. Find the empirical probability that a candidate has less than four errors in the typed manuscript.

Answer :

MRROYALGO

Answer:

The probability that a candidate has less than 4 errors is 0.40

Step-by-step explanation:

Given

[tex]n(S)= 20[/tex] --- candidates

See attachment for histogram

Required

[tex]P(x < 4)[/tex]

From the attached histogram, the errors less than 4 are: 0 or 1 and 2 or 3

And the corresponding frequencies are: 5 and 3, respectively.

So:

[tex]P(x < 4) = P(0\ or\ 1) + P(2\ or\ 3)[/tex]

This gives:

[tex]P(x < 4) = \frac{n(0\ or\ 1)}{n(S)} + \frac{n(2\ or\ 3)}{n(S)}[/tex]

Substitute 5, 3 and 20 for n(0 or 1), n(2 or 3) and n(S), respectively

[tex]P(x < 4) = \frac{5}{20} + \frac{3}{20}[/tex]

Take LCM

[tex]P(x < 4) = \frac{5+3}{20}[/tex]

[tex]P(x < 4) = \frac{8}{20}[/tex]

[tex]P(x < 4) = 0.40[/tex]

View image MRROYAL

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