4 Suppose the weights of Golden Retrievers are normally dist

4. Suppose the weights of Golden Retrievers are normally distributed with a mean of 64 lbs and a standard deviation of 4 lbs. a) What proportion of Golden Retriever weighs between 58 lbs and 70 lbs ? b) what proportion of Golden Retrievers weigh more than 72 pounds? c) 80% of Golden Retrievers weigh more than

Solution

Suppose the weights of Golden Retrievers are normally distributed with a mean of 64 lbs and a standard deviation of 4 lbs.

Z value for 58, z = (58- 64)/4 =-1.5

Z value for 70, z = (70- 64)/4 =1.5

P( 58 <X<70)= P(-1.5<z<1.5) =

=p(z<1.5 ) - P(z < -1.5) = 0.9332 - 0.0668 =0.8664

Z value for 72, z = (72- 64)/4 = 2

P( x>72) = P(z>2) = 0.0228

c) 80% of Golden Retrievers weigh more than __________

z value for more than 80% values = -0.842

The required value = 64 - 0.842*4 = 60.632