Question

# The weights of a certain dog breed are approximately normally distributed with a mean of 53...

The weights of a certain dog breed are approximately normally distributed with a mean of 53 pounds, and a standard deviation of 5.9 pounds. 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 53 pounds. %
b) Find the percentage of dogs of this breed that weigh less than 49 pounds. %
c) Find the percentage of dogs of this breed that weigh more than 49 pounds. %

Solution :

Given that,

mean = = 53

standard deviation = = 5.9

P(X<53 ) = P[(X- ) / < (53-53) /5.9 ]

= P(z < 0)

Using z table

= 0.500

=50%

B.

P(X<49 ) = P[(X- ) / < (49-53) /5.9 ]

= P(z < -0.68)

Using z table

= 0.2483

=24.83%

C.

P(X>49 ) =1 - P[(X- ) / < (49-53) /5.9 ]

= P(z < -0.68)

Using z table

= 1 - 0.2483

=0.7517

=75.17%

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