Question

The yield of a chemical process is being studied. From previous experience, yield is known to be normally distributed and σ=3. The past five days of plant operation have resulted in the following yields 91.6, 88.75, 90.8, 89.61, and 91.3. Find a 95% two-sided confidence interval on the true mean yield.

(a) Calculate the sample mean. Round your answer to 2 decimal places.

x¯=

(b) Calculate the 95% two-sided confidence interval on the true mean yield. Round your answers to 1 decimal place.

___ ≤μ≤ ___

Answer 1

From the given data,

Here,

given values 91.6,88.75,90.8,89.61,91.3
(a) sample mean X = 90.41

(b)95% confidence for z is 1.96
standard deviation given is 3
confidence interval formula
=> x +/- z * s/sqrt(n)
=> 90.41 +/- 1.96 * 3/sqrt(5)
=> 87.8 < μ < 93.0