Question

Help Please?!?

Pearls from a commercial oyster bed are distributed normally in diameter, with an average of 5 mm, and a standard deviation of 0.5 mm. A new section is started and the nutrient mix to the oysters is changed. What is the average size the pearls from the new bed must be so that the company has 95% confidence that the new mix leads to bigger pearls?

anything over 5 mm
over 5.8 mm
at least 4 mm
at least 6 mm

Answer 1

Note that the population mean, the population std. dev., the level of confidence and the sample size are all given in the problem statement. Can you now finish this problem?
What is the z-critical-value for 98% confidence?

Answer 2

\[\mu \pm z _{critical ~value}\frac{ \ \sigma }{ \sqrt{n} } \]