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Y_Kistochka [10]
2 years ago
10

A survey of students at a particular college showed that 33% of them prefer the American Heritage Dictionary (as opposed to Webs

ter’s or Random House). If 30 students are randomly surveyed, find the probability that exactly 6 of them prefer the American Heritage Dictionary.
Mathematics
1 answer:
Juliette [100K]2 years ago
7 0

Answer:

5.13 % to the nearest hundredth.

Step-by-step explanation:

This is a Binomial Distribution .

The required probability

= 30C6 (0.33)^6 (0.67)^(30-6)

= 0.051345

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bagirrra123 [75]
\bf r\left[ cos\left(  \theta \right)+i\ sin\left( \theta  \right) \right]\quad &#10;\begin{cases}&#10;x=rcos(\theta )\\&#10;y=rsin(\theta )&#10;\end{cases}\implies &#10;\begin{array}{llll}&#10;x&,&y\\&#10;a&&b&#10;\end{array}\implies a+bi\\\\&#10;-------------------------------\\\\&#10;2\left[ cos\left(  135^o\right)+i\ sin\left( 135^o\right) \right]\impliedby r=2\qquad \theta =135^o&#10;\\\\\\&#10;2\left( -\frac{\sqrt{2}}{2} \right)+i\ 2\left( \frac{\sqrt{2}}{2}\right)\implies -\sqrt{2}+\sqrt{2}\ i

\bf -------------------------------\\\\&#10;3\left[ cos\left(  120^o\right)+i\ sin\left( 120^o\right) \right]\impliedby r=3\qquad \theta =120^o&#10;\\\\\\&#10;3\left( -\frac{1}{2} \right)+i\ 3\left( \frac{\sqrt{3}}{2}\right)\implies -\frac{3}{2}+\frac{3\sqrt{3}}{2}\ i

\bf \\\\&#10;-------------------------------\\\\&#10;5\left[ cos\left(  \frac{5\pi }{4}\right)+i\ sin\left( \frac{5\pi }{4}\right) \right]\impliedby r=5\qquad \theta =\frac{5\pi }{4}&#10;\\\\\\&#10;5\left( -\frac{\sqrt{2}}{2} \right)+i\ 5\left( -\frac{\sqrt{2}}{2}\right)\implies -\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\ i

\bf -------------------------------\\\\&#10;4\left[ cos\left(  \frac{5\pi }{3}\right)+i\ sin\left( \frac{5\pi }{3}\right) \right]\impliedby r=4\qquad \theta =\frac{5\pi }{3}&#10;\\\\\\&#10;4\left( \frac{1}{2} \right)+i\ 4\left( -\frac{\sqrt{3}}{2}\right)\implies \frac{1}{2}-\frac{\sqrt{3}}{2}\ i
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