The mean incubation time for a type of fertilized egg kept at 100.1 F is 20 days

Question

The mean incubation time for a type of fertilized egg kept at 100.1 F is 20 days. Suppose that the incubation times are approximately normally 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? (round to 4 decimal places)

B) What is the probability that a randomly selected fertilized egg hatches between 16 and 20 days? (round to 4 decimal places)

C) What is the probability that a randomly selected fertilized egg takes over 22 days to hatch? (round to 4 decimal places)

Explanation / Answer

(A) What is the probability a randoly selected egg hatches in less than 18 days?

Construct your test statistic:

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) What is the probability that a randomly selected fertilized egg hatches between 16 and 20 days
Construct your test statistic:

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

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