Question

Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 2.3 pounds and a standard deviation of 0.9 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 = = 2.3

standard deviation = = 0.9

n = 3

= 2.3 and

= / n = 0.9 / 3 = 0.5196

a)

P( < 1.0) =   P(( - ) / < (1 - 2.3) / 0.5196)

= P(z < -2.50)   Using standard normal table.   

Probability = 0.0062

b)

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

= 1 - P(( - ) / < (3 - 2.3) / 0.5196)

= 1 - P(z < 1.35)

= 1 - 0.9115 Using standard normal table.

= 0.0885

Probability = 0.0885