Question

# The weights of a certain dog breed are approximately normally distributed with a mean of 50...

The weights of a certain dog breed are approximately normally distributed with a mean of 50 pounds, and a standard deviation of 6.6 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 47 pounds. ______ %

c) Find the percentage of dogs of this breed that weigh more than 47 pounds. ______ %

Solution :

Given that,

mean = = 50

standard deviation = = 6.6

P(X<50 ) = P[(X- ) / < (50-50) /6.6 ]

= P(z < 0)

Using z table

= 0.5000

=50.00%

b

P(X<47 ) = P[(X- ) / < (47-50) /6.6 ]

= P(z < -0.45)

Using z table

=0.3264

=32.64%

c

P(X>47 ) =1 - P[(X- ) / > (47-50) /6.6 ]

= 1 -P(z < -0.45)

Using z table

= 1 -0.3264

=0.6736

=67.36%

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