Question

A ranch in "Smart Town" claimed that the cows they raise are smarter than the rest of the population of US cows. To prove that they announced that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams. Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation=64 g. a) What is the Probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams b) What is the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams

Answer 1

Solution :

Given that ,

mean = = 485

standard deviation = = 64

a) P(x 500 ) = 1 - P(x   500 )

= 1 - P[(x - ) / (500 - 485) /64 ]

= 1 -  P(z 0.23 )  

= 1 -0.0591 = 0.4090

Probability = 0.4090

b)

n = 36

= = 485

= / n = 64/ 36 = 10.6667

P( 480 ) = 1 - P( 480 )

= 1 - P[( - ) / (480 -485) /10.6667 ]

= 1 - P(z -0.47 )

= 1 - 0.3192 = 0.6808

Probability = 0.6808