Question

The mean incubation time of fertilized eggs is 23 days, Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day (a) Determine the 20th percentile for incubation times. (b) Determine the incubation times that make up the middle 95%. Click the icon to view a table of areas under the normal curve. (a) The 20th percentle for incubation times is 22 days. (Round to the nearest whole number as needed.) (b) The incubation times that make up the middle 95% are to days. Round to the nearest whole number as needed. Use ascending order.)

Answer 1

(a)

$\mu$ = 23

$\sigma$ = 1

20th percentile corresponds to area = 0.50 - 0.20 = 0.30 from mid value to Z on LHS.

Table of Area Under Standard Normal Curve gives Z = - 0.84

So,

Z = - 0.84 = (X - 23)/1

So,

X = 23 - 0.84 = 22.16

So,

Answer is:

22

(b) Middle 95% corresponds to area = 0.95/2 = 0.475 on either side of mid value.

Table of Area Under Standard Normal Curve gives Z = $\pm$ 1.96

Low Side:
Z = - 1.96 = (X - 23)/1

So,

X = 23 - 1.96 = 21.84

High Side:
Z = 1.96 = (X - 23)/1

So,

X = 23 + 1.96 = 24.96

So,

Answer is:

22 to 25