the mean incubation time for a type of fertilized egg kept 100.2degrees f is 20

Question

the mean incubation time for a type of fertilized egg kept 100.2degrees f is 20 days. suppose that the incubation times are approximately normal distributed with a standard deviation of 2 days.

a. What is the probability that a randomly selected fertilized egg hatches in less than 18 days?

b. What is the probablility that a randomly selected fertilized egg takes over 22 days to hatch is?

c. the probability that a randomly selected ferilized egg hatches between 16 and 20 days is?

d. Would it be unusual for an egg to hatch in less than 15 days?

Explanation / Answer

(a)

P(< 18 days)

z< (x-?)/?

z < (18-20)/2

z<-1

Using a probability table (remember- this is one-sided), this corresponds to p = 0.1587.

b)

Construct your test statistic:

P(> 22 days)

z > (22-20)/2

z<1

Using a probability table (remember- this is one-sided), this corresponds to p = 0.1587.

c) P(16<x< 20 days)

(16-20)/2 <z (20-20)/2

-2<z<0

This means we calculate

P(z<0) - P(z<-2)

= 0.5000 - 0.0228

= 0.4772

d)

P(X<15) = P(Z<(15-20)/2)

=P(Z<-2.5) = 0.0062

Since the proability is less than 0.05, it would be unusual for an egg to hatch in less than 15 days

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