Question

An apple juice producer buys all his apples from a large orchard. the amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. suppose a sample of 25 apples is selected, what is the probability that the sample mean will be at least 4.60 ounces?

Answer 1

$$P(x> 4.60) = P(z > \frac {4.60-4.70} {\frac {0.40} {\sqrt25}})$$ $$= P(z > -1.25) = 1- P(z< -1.25)$$

$$= 1-0.1056 = 0.8944$$ $$P (x > 4.60) =0.8944$$