Question

The weight of Idaho potatoes are normally distributed with a mean of 15 oz and a standard deviation of 1.8 oz. Find the following probabilities: a)    P(12<W<19), P(W>17.8), P(W<14.8) b) you are selecting a sample of 16 Idaho potatoes find P(average weight>17.2), c) Is it unusual to find a sample of 16 Idaho potatoes with an average weight =14.8 o

Answer 1

a)

P(12<W<19) =P((12-15)/1.8<Z<(19-15)/1.8) =P(-1.67<Z<2.22) =P(Z<2.22)-P(Z<-1.67) =0.9868-0.0475 =0.9393 (by using normal table) =0.9391 (by using calculator)

P(W>17.8) =P(Z>(17.8-15)/1.8) =P(Z>1.56) =1-P(Z<1.56) =1-0.9406 =0.0594 (by normal table) =0.0599 (by calculator)

P(W<14.8) =P(Z<(14.8-15)/1.8) =P(Z<-0.11) =0.4562 (by normal table) =0.4558 (by using caclulator)

$\\ Standard\ deviation\ of\ average\ weight\ of\ 16\ ladho \ potatoes \\\\ =\frac{1.8}{\sqrt{16}}=\frac{1.8}{4}=0.45$

b)

P(average weight>17.2)
=P(Z>(17.2-15)/0.45)
=P(Z>4.89)
=1-P(Z<4.89)
=0.000000507

c)

$\\ z\ score\ for\ average\ weight \ 14.8\ is \\\\ \frac{15-14.8}{0.45}=0.4444\\ \\ is\ is\ between\ -1.96\ to\ 1.96\\ \\ So,\ it\ is\ not \ unusual$