Since the sample standard deviation is now known, we use
the z-score test. The formula is given as:
z= (X – μ) / (s / sqrt(n))
Where,
X = sample mean = 8.6 lb to 14.6 lb
μ = population mean = 11 lb
s = population standard deviation = 6
n = sample size = 4
1st: Calculating for z when x = 8.6 lb
z = (8.6 – 11) / (6 / sqrt4)
z = - 0.8
Using the standard distribution table for z:
Probability (x = 8.6
lb) = 0.2119
2nd: Calculating for z when x = 14.6 lb
z = (14.6 – 11) / (6 / sqrt4)
z = 1.2
Using the standard distribution table for z:
Probability (x = 14.6
lb) = 0.8849
Therefore
the probability that the mean weight will be between 8.6 and 14.6 lb:
Probability (8.6 ≤ x ≤ 14.6 ) = 0.8849 - 0.2119
Probability (8.6 ≤ x <span>≤ 14.6 ) = 0.673 (ANSWER)</span>
