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 6.07 ounces and a standard deviation of 0.1 ounce. suppose that you draw a random sample of 33 cans. find the probability that the mean weight of the sample is less than 6.02 ounces.

0.0021

Step-by-step explanation:

Mean weight = u = 6.07 ounce

Standard deviation = = 0.1 ounce

Sample size = n = 33

Test value = x = 6.02

We need to find the probability that mean weight of the sample is less than 6.0 ounces. Mathematically this can be expressed as:

P(x < 6.02)

In order to find this probability we need to convert this value to z-score. The formula to calculate the z score for the sample is:

Using the values, we get:

Thus, the probability that mean weight of the sample is less than 6.0 ounces is equivalent to P( z < - 2.87 )

i.e.

P(x < 6.02) = P( z < - 2.87 )

From the z table, the probability of z score being less than -2.87 comes out to be 0.0021

So,

P(x < 6.02) = 0.0021

Therefore, the probability that the mean weight of the sample is less than 6.02 ounces is 0.0021