Question

The time it takes duck eggs to hatch in a nursery is normally distributed with a meanof 42 days and a standard deviation of 3.8 days. What is the probability that arandomly selected duck egg takes between 34 and 43 days to hatch?

Answer 1

The time it takes duck eggs to hatch in a nursery is normally distributed with a mean

of 42 days and a standard deviation of 3.8 days. What is the probability that a

randomly selected duck egg takes between 34 and 43 days to hatch?

step 1

Find the z-scores

For x=34

z=(34-42)/3.8

z=--2.105

For x=43

z=(43-42)/3.8

z=0.263

step 2

using Standard Normal Distribution Table

we have

For z=-2.105 --------> P=0.4842

For z=0.263 -------> P=0.1026

therefore

the probability is

P=0.4842+0.1026=0.5868