Question

The weights of a certain dog breed are approximately normally distributed with a mean of 50 pounds, and a standard deviation of 6 pounds. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.

a) Find the percentage of dogs of this breed that weigh less than 50 pounds. %
b) Find the percentage of dogs of this breed that weigh less than 48 pounds. %
c) Find the percentage of dogs of this breed that weigh more than 48 pounds. %

Answer 1

Since the distribution is normal hence to calculate percentage we need to find Z score and percentage accordingly using Z table.

a) P( X<50)

Z at X=50

Hence below 50 the Percentage will be 50 % as it lirs at the mean,

b) P(X<48)

Using z table shown below

P(X<48) =P(Z<-0.33)

=0.3707

c) P(X>48)

P(X>48)=P(Z>-0.33)

=1-0.3707

=0.6293