Respuesta :

Answer:  C)  0.16

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Explanation:

Convert the x = 82 to a corresponding z score.

z = (x-mu)/sigma

z = (82 - 89)/7

z = -7/7

z = -1

Using the empirical rule (see chart below), roughly 68% of the distribution is within 1 standard deviation of the mean.

This leaves 1 - 0.68 = 0.32 = 32% of the distribution in both tails, and (32%)/2 = 16% of the area is in one tail, which converts to 0.16

About 16% of the normally distributed population is below z = -1.

So we can say [tex]P(x \le 82) = P(z \le -1) \approx 0.16[/tex]

Ver imagen jimthompson5910
  • Mean=[tex]\overline{x}[/tex]=89
  • Standard deviation=[tex]\sum[/tex]=7

  • x is 82

z value:-

[tex]\\ \rm\Rrightarrow \dfrac{x-\overline{x}}{\sum}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{82-89}{7}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{-7}{7}[/tex]

[tex]\\ \rm\Rrightarrow -1[/tex]

  • z=-1

As per z value chart

  • Part distributed to z=-1 is 32%/2=16%=0.16

Option C is correct

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