The mean incubation time for a type of fertilized egg kept at 100.6 F is 20 days

Question

The mean incubation time for a type of fertilized egg kept at 100.6 F is 20 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 22 days. (a) What is the probability that a randomly selected fertilized egg hatches in less than 16 days? (b) What is the probability that a randomly selected fertilized egg takes over 24 days to hatch? (c) What is the probability that a randomly selected fertilized egg hatches between 18 and 20 days? (d) Would it be unusual for an egg to hatch in less than 14 days? Why? The probability of this event is _______, so it would/would not be unusual because the probability is less/greater than 0.05. (Round to four decimal places as needed.)

Explanation / Answer

Given, mean(() = 20 days,

standard deviation()= 22 days,

(a). P(< 16 days)

z< (x-)/

z < (16-20)/22
z<-2/11
Using a probability table (remember- this is one-sided), this corresponds to p = 0.4286.

(b). P(> 24 days)
z > (24-20)/22
z<2/11
Using a probability table (remember- this is one-sided), this corresponds to p = 0.5714.

(c). P(18<x< 20 days)
(18-20)/22 < z < (20-20)/22
(-1/11) < z < 0
This means we calculate
P(z<0) - P(z<-1/11)
= 0.5000 - 0.4641
= 0.0359

(d). It depends what you mean by unusual.

t = 14 days corresponds to a z score of

z = (14-20)/22 = -0.27

which means a probability of 0.3936
If you use a threshold of =0.10 (10%) as "unusual", then yes, it is. However, it is more typical to use an = 0.05, in which case this doesn't count as unusual.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.