Question

The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.2 ounces and a standard deviation of 0.11 ounce. Suppose that you draw a random sample of 37 cans. Find the probability that the mean weight of the sample is less than 6.19 ounces.

Answer 1

Solution :

Given that ,

mean = = 6.2

standard deviation = = 0.11

n = 37

= 6.2

=  / n = 0.11/ 37=0.018

P( < 6.19) = P[( - ) / < (6.19-6.2) / 0.018]

= P(z < -0.56)

Using z table  

probability = 0.2827