Question

The amount of meat on a Subbies foot-long sub follows a Normal distribution, with a mean of 8 ounces and a standard deviation of 0.6 ounce. A random sample of 25 subs is selected every day and measured. What is the probability that the mean weight will exceed 8.2 ounces?

Answer 1

95.15%

Explanation:

We have that the mean (m) is equal to 8, the standard deviation (sd) 0.6 and the sample size (n) = 25

They ask us for P (x <8.2)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (8.2 - 8) / (0.6 / (25 ^ 1/2))

z = 1.66

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <1.66) = 0.9515

It means that the probability that it exceeds 8.2 ounces is 95.15%