or Ameras beleve that recycling trash makes the biggest difference in protecting

Question

or Ameras beleve that recycling trash makes the biggest difference in protecting the to save Snapnet for, mat about protecting Suppose a rendam sample of -60 aus are polied and asked if they believed that recycing made the biogest ifference in protecting our environment. Let u that a) Fewer than 36 individuals believe that recycling makes the biggest ofference? 10 More than 47 Indivituals believe that necycing makes the biggest difference? (c) Mane than 13 individuals believe that recying does not make the biggest difference aseroprane appendix table or Need Help?

Explanation / Answer

For a sample of n = 60 adults and we assume that the 78% figure is right, thus :

We take the mean value of the individuals that say recycling makes the biggest difference = 78% of 60 = 46.8

By the normal approximation, Variance = np(1-p) = (60)(0.78)(0.22) = 10.296

Standard deviation = (Variance)0.5 = 3.21

(a)

P ( X < 36 ) :

Z = X - mean / SD = 36 - 46.8 / 3.21 = -3.36

P (X < 36) = P(Z < -3.36) = 0.0004

(b)

P (X > 47) :

P (X > 47) = 1 - P( X <= 47)

Z = 47 - 46.8 / 3.21 = 0.06

P(X <= 47) = P(Z <= 0.06) = 0.524

P (X > 47) = 1 - 0.524

P (X > 47) = 0.476

(c)

P (X > 13) :

P (X > 13) = 1 - P( X <= 13)

Z = 13 - 46.8 / 3.21 = -10.53

P(X <= 13) = P(Z <= -10.53) = 0.0001

P (X > 13) = 1 - 0.0001

P (X > 47) = 0.9999

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