Question

(1 point) 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 6.19 ounces and a standard deviation of 0.23 ounce. Suppose that you draw a random sample of 37 cans. Find the probability that the mean weight of the sample is less than 6.14 ounces. Probability =

Answer 1

Solution :

$\sigma$
_T
= $\sigma$ / $\sqrt$ n = 0.23 / $\sqrt$ 37 = 0.0378

P(
T
< 6.14) = P((
T
- $\mu$
_T
) / $\sigma$
_T
< (6.14 - 6.19) / 0.0378)

= P(z < -1.32)

= 0.0934

Probability = 0.0934