The mean incubation time of fertilized eggs is 21days. Suppose the incubation times are approximately normally distributed with a standard deviation of 11day.
(b) Determine the incubation times that make up the middle 97%.
Given that,
mean =
= 21
standard deviation =
= 11
middle 97% of score is
P(-z < Z < z) = 0.97
P(Z < z) - P(Z < -z) = 0.97
2 P(Z < z) - 1 = 0.97
2 P(Z < z) = 1 + 0.97 =1.97
P(Z < z) =1.97 / 2 = 0.985
P(Z <2.17 ) = 0.985
z ± 2.17 using standard normal (Z) table
Using z-score formula
x= z *
+
x= -2.17*11+21
x= 2.87
z = 2.17
Using z-score formula
x= z *
+
x= 2.17*11+21
x= 44.87
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