Question

The mean incubation time of fertilized eggs is 22 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​% of fertilized eggs.

Answer 1

Solution :

mean = = 22

standard deviation = = 1

Using standard normal table,

(a)

P(Z < z) = 11% = 0.11

P(Z < -1.227) = 0.11

z = -1.227

Using z-score formula,

x = z * +

x = -1.227 * 1 + 22 = 20.773

11th percentile = 20.77

(b)

P(Z < z) = 39% = 0.39

P(Z < -0.28) = 0.39

z = -0.28

Using z-score formula,

x = z * +

x = -0.28 * 1 + 22 = 21.72

P(Z > z) = 0.39

1 - P(Z < z) = 0.39

P(Z < z) = 1 - 0.39 = 0.61

P(Z < 0.28) = 0.61

z = 0.28

x = 0.28 * 1 + 22 = 22.28

Incubation times = 21.72 and 22.28