Because you know the population standard deviation and know the population follows a normal distribution, you can use the ztest.
(A) What is the probability a randoly selected egg hatches in less than 18 days?
Construct your test statistic:
P(< 18 days)
z< (xμ)/σ
z < (1819)/1
z<1
Using a probability table (remember this is onesided), this corresponds to
p = 0.1587.
(B) What is the probability a randomly selected egg hatches takes over 20 days?
Construct your test statistic:
P(> 20 days)
z > (2019)/1
z<1
Using a probability table (remember this is onesided), this corresponds to
p = 0.1587.
(C) What is the probabilty that randomly selected fertilized eggs hatches 17 and 19 days?
Construct your test statistic:
P(17<x< 19 days)
(1719)/1 <z (1919)/1
2<z<0
This means we calculate
P(z<0)  P(z<2)
= 0.5000  0.0228
= 0.4772
(D) Would it be unusual for an egg to hatch in less than 17.5 days and why?
Ugh. It depends what you mean by unusual.
t = 17.5 days corresponds to a z score of
z = (17.519)/1 = 1.5
which means a probability of 0.0668.
If you use a threshold of α=0.10 (10%) as "unusual", then yes, it is. However, it is more typical to use an α = 0.05, in which case this doesn't count as unusual.
11/24/2013

Ryan Y.