Question

Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.8 pounds.

(a) If you catch 3 random bass from Clear Lake, find the probability that the mean weight is less than 1.0 pound. Round your answer to 4 decimal places.


(b) If you catch 3 random bass from Clear Lake, find the probability that the mean weight it is more than 3 pounds. Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 1.9

standard deviation = = 0.8

n =3

= 1.9

= / n = 0.8 / 3 =0.4619

(a)P( <1.0 ) = P(( - ) / < (1.0 - 1.9) /0.4619 )

= P(z < -1.95)

Using z table

= 0.0256   

(b)P( >3 ) = 1 - P( <3 )

= 1 - P[( - ) / < (3 - 1.9) /0.4619 ]

= 1 - P(z <2.38 )

Using z table,    

= 1 - 0.9913

= 0.0087