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 5.97 ounces and a standard deviation of 0.23 ounce. Suppose that you draw a random sample of 34 cans. Find the probability that the mean weight of the sample is less than 5.94 ounces.

Answer 1

Solution :

Given that ,

mean = = 5.97

standard deviation = = 0.23

n = 34

=   = 5.97

= / n = 0.23 / 34 = 0.0394

P( < 5.94) = P(( - ) / < (5.94 - 5.97) /0.0394 )

= P(z < -0.76 )

= 0.2236

probability =0.2236