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Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly​ selected, find the probability that they have a mean height between 63 and 65 inches.

Respuesta :

thaovtp1407

Answer:

0.9812

Step-by-step explanation:

We need to find the z-score of 63 and of 65:

  • z(63)=(63-63.6)/[2.5/[tex]\sqrt{75}[/tex]]=-2.07846...
  • z(65)=(65-63.6)/[2.5/[tex]\sqrt{75}[/tex]]=4.8497...

=> P(-2.07846[tex]\leq[/tex]Z[tex]\leq[/tex]4.8497)=0.9812

So the probability that they have a mean height between 63 and 65 inches is 0.9812

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