The mean incubation time of fertilized eggs is 21 days. Suppose the incubation t

Question

The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 11th percentile for incubation times. (b) Determine the incubation times that make up the middle 39%. (a) The 11th percentile for incubation times is 20 days. (Round to the nearest whole number as needed.) (b) The incubation times that make up the middle 39% are to days. (Round to the nearest whole number as needed. Use ascending order.)

Explanation / Answer

a) P(X< X*) = 0.11

Z = (X - 21)/1

P(Z<Z*) = .11

Z* = -1.227

hence X* = 21 - 1.227 = 19.773 = 20

b) middle 39 %

39/ 2 % = 0.198

0.5 -0.198 = 0.302

0.5 + 0.198 = 0.698

P(Z< Z* ) = 0.698

z* = 0.518

hence

lower - 21 - 0.518 *1 = 20.482 = 20

upper 21 + 0.518 *1 = 21.518 = 22

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